# Previous seminars at the Landau Institute scientific council

## Bound pairs of "magnetic skyrmion – superconducting vortex" in thin bilayers

20 January in 11:30

S. Apostoloff, E. Andriaykhina, P. Vorobyev, O. Tretiakov, I. Burmistrov

In a recent paper [Phys. Rev. B 103, 174519 (2021)] it has been theoretically shown that a Néel magnetic skyrmion and a superconducting Pearl vortex can form bound pairs in bilayers of the superconductor and ferromagnetic thin films due to the stray fields. Depending on the parameters of the system, the centers of the skyrmion and the vortex can be located either strictly above each other or at a finite distance of the order of the skyrmion radius. However, the analysis in that paper was limited to the main order of the perturbation theory in the magnetic field of the vortex. The report will present a more detailed study of such bound pairs in systems in which stabilization of the skyrmion is determined by the Dzyaloshinskii–Moriya interaction. Firstly, it will be shown that with an increase in the effective strength of the vortex, a counterintuitive phenomenon occurs: the repulsion between the skyrmion and the vortex is suppressed, and the distance between their centers decreases [JETP Letters, 116(11), 801-807 (2022) / arXiv:2210.08790]. Secondly, for the coaxial skyrmion and vortex, a significant change of the skyrmion is predicted: the chirality can change and/or the radius can increase significantly. In addition, with the same heterostructure parameters, but depending on the initial magnetization distribution in a ferromagnet, up to three different bound pairs of "skyrmion – vortex" can arise, where one skyrmion has negative chirality, and the other two have different radii and positive chirality [arXiv:2212.08351 / submitted to PRL].

## Comment on "Super-universality in Anderson localization"

30 December 2022 in 11:30 (short)

I.S. Burmistrov

Comment on recent paper by I. Horváth and P. Markoš, "Super-universality in Anderson localization", Phys. Rev. Lett. 129, 106601 (2022) [arXiv:2110.11266]
Details can be found in arXiv:2210.10539

## The first signal of jet quenching in pp collisions

23 December 2022 in 11:30 (short)

B.G. Zakharov

We discuss jet quenching in mini quark-gluon plasma produced in $pp$ collisions. We study the modification factor $I_{pp}$, describing the medium modification of the jet fragmentation functions. We calculate $I_{pp}$ within the light-cone path integral approach to induced gluon emission for parametrization of the running coupling $\alpha_s(Q,T)$ which has a plateau around $Q=\kappa T$, motivated by the lattice calculations of the effective QCD coupling in the quark-gluon plasma. We calculate $I_{pp}$ with no free parameters using $\kappa$ fitted to the LHC data on the nuclear modification factor $R_{AA}$. We find that the predicted decrease with multiplicity of $I_{pp}$ for $5.02$ TeV $pp$ collisions agrees reasonably with the recent preliminary data from ALICE. Our results show that the drop of $I_{pp}$ with the multiplicity, if confirmed by further measurements, may be viewed as the first direct evidence for jet quenching in $pp$ collisions.

## Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point

23 December 2022 in 11:30

P.A. Nosov, I.S. Burmistrov, S. Raghu

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that: (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called Cooperons') acquire anomalous dynamical scaling z=4, indicating strong non-Fermi liquid behaviour.

## Long-range interactions between membrane inclusions: Electric field induced giant amplification of the pairwise potential

16 December 2022 in 11:30

E.S. Pikina, A.R. Muratov, E.I. Kats, V.V. Lebedev

The aim of this work is to revisit the phenomenological theory of the interaction between membrane inclusions, mediated by the membrane fluctuations. We consider the case where the inclusions are separated by distances larger than their characteristic size. Within our macroscopic approach a physical nature of such inclusions is not essential. However, we have always in mind two prototypes of such inclusions: proteins and RNA macromolecules. Because the interaction is driven by the membrane fluctuations and the coupling between inclusions and the membrane, it is possible to change the interaction potential by external actions affecting these factors. As an example of such external action we consider an electric field. Under external electric field (both dc or ac), we propose a new coupling mechanism between inclusions possessing dipole moments (as it is the case for most protein macromolecules) and the membrane. We found, quite unexpected and presumably for the first time, that the new coupling mechanism yields to giant enhancement of the pairwise potential of the inclusions. This result opens up a way to handle purposefully the interaction energy, and as well to test of the theory set forth in our article.
Results are published in Annals of Physics 447(Pt.2), 168916 (2022); https://doi.org/10.1016/j.aop.2022.168916

## The structure of angular diagrams for systems describing the dynamics of an electron in a magnetic field for dispersion laws in general position

16 December 2022 in 11:30 (short)

I.A. Dynnikov, A.Ya. Maltsev, S.P. Novikov

We present a number of results that significantly refine the description of the angular diagrams that arise in the study of the dynamics of an electron in a magnetic field at all energy levels simultaneously. The description allows us to introduce some hierarchical structure on the set of stability zones on such diagrams, as well as to describe in more detail the set of occurrence of complex (chaotic) trajectories of the corresponding dynamical system. ZhETF, Volume 162, Issue. 2 (2022), UMN, volume 77, issue 6(468) (2022)

## Open level lines of a superposition of periodic potentials on a plane

16 December 2022 in 11:30 (short)

A.Ya. Maltsev, S.P. Novikov

We study the geometry of open potential level lines arising from the superposition of two different periodic potentials on a plane. This problem can be considered as a particular case of the Novikov problem on the behavior of open level lines of quasi-periodic potentials on a plane with four quasi-periods. At the same time, the formulation of this problem can have many additional features. We will give a general description of the emerging picture both in the most general case and in the presence of additional restrictions. The main approach to describing the behavior of open level lines is based on their division into topologically regular and chaotic level lines. Annals of Physics, In Press, Corrected Proof, Available online 22 July 2022, art. 169039; arXiv:2206.04014

## NSR singular vectors from Uglov polynomials

9 December 2022 in 11:30 (short)

Mikhail Bershtein

It was conjectured in 2012 that bosonization of a singular vector (in the Neveu–Schwarz sector) of the N=1 super analog of the Virasoro algebra can be identified with the Uglov symmetric function. We prove this conjecture. We also extend this result to the Ramond sector of the N=1 super-Virasoro algebra.
Based on joint work: M. Bershtein, A. Vargulevich, "NSR singular vectors from Uglov polynomials", J. Math. Phys. 63, 061706 (2022), arXiv:2202.11810.

## Semiclassical approach to calculation of form factors in the sinh-Gordon model

2 December 2022 in 11:30

M. Lashkevich, O. Lisovyy, T. Ushakova

Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter $b$ on the background of a radial symmetric classical solution. For this purpose we use a generalization of the radial quantization, well known for a massless boson field. We obtain new special functions, which generalize the Bessel functions and have an interesting interpretation in the theory of the classical sinh-Gordon model. The form factors of the exponential operators are completely determined by classical solutions in the leading order, while the form factors of descendant operators contain quantum corrections even in the leading order. Consideration of descendant operators in two chiralities demands renormalizations, which are analogous to those in the conformal perturbation theory.

## Bogoyavlensky lattices and the generalized Catalan numbers

2 December 2022 in 11:30 (short)

Several years ago A.B. Shabat proposed the problem on the decay of the unit step solution for the Volterra lattice terminated on a half-line. It is resembling the Gurevich-Pitaevsky problem on the step-like solutions for the KdV equation, but it turned out to be simpler since the answer is found explicitly. One solution method is based on the observation that the Taylor series for the tau function of the lattice equation serves as the exponential generating function for the Catalan numbers and is expressed in terms of a hypergeometric function. This can be proved using the well-known result in combinatorics that the Hankel transform for the Catalan numbers is the identity sequence. The second method uses a finite-dimensional reduction associated with the master-symmetry of the lattice; the solution with the unit step initial data is contained within this reduction. This talk is about similar results on the relations between the Bogoyavlensky lattices, the generalized Catalan numbers (known in combinatorics) and the generalized hypergeometric functions.

## Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling

25 November 2022 in 11:30

E.S. Andriyakhina, I.S. Burmistrov

The interplay of Anderson localization and electron-electron interactions is known to lead to enhancement of superconductivity due to multifractality of electron wave functions. We develop the theory of multifractally-enhanced superconducting states in two-dimensional systems in the presence of spin-orbit coupling. Using the Finkel'stein nonlinear sigma model, we derive the modified Usadel and gap equations that take into account renormalizations caused by the interplay of disorder and interactions. Multifractal correlations induce energy dependence of the superconducting spectral gap. We determine the superconducting transition temperature and the superconducting spectral gap in the case of Ising and strong spin orbit couplings. In the latter case the energy dependence of superconducting spectral gap is convex whereas in the former case (as well as in the absence of spin-orbit coupling) it is concave. Multifractality enhances not only the transition temperature but, in the same way, the spectral gap at zero temperature. Also we study mesoscopic fluctuations of the local density of states in the superconducting state. Similarly to the case of normal metal, spin-orbit coupling reduce the amplitude of fluctuations.
Results are reported in E.S. Andriyakhina, I.S. Burmistrov, ZhETF 162, 522 (2022).

## Non-Abelian generalizations of Painlev´e systems

25 November 2022 in 11:30 (short)

V.V. Sokolov

The report is devoted to the problem of classifying integrable matrix systems of the Painlevé equations P_2-P_6 type. Using the Kovalevskaya-Painlevé test, all integrable matrix systems of type P_4 are found. All systems of types 2-6 are found that have matrix generalizations of the Okamoto Hamiltonians. All integrable matrix Hamiltonian systems of types P_2-P_6 are described.

## Inverse cascade spectrum of gravity waves on the surface of a fluid in the presence of condensate: analytical explanation.

25 November 2022 in 11:30 (short)

Alexander Korotkevich, Sergey Nazarenko

Previously it was reported that universal spectrum of the inverse cascade of gravity waves on the surface of 3D fluid in the presence of condensate is different from the KZ-spectrum predicted by the Wave Turbelence Theory. Anflytical explanation of the difference in the spectrum slope is proposed. Interaction of short waves with a long wave backgrown (condensate) was considered in the framework of diffusion approximation for the Hasselmann waves kinetic equation. "Diffusion" coefficient in the wavenumbers space was obtained as a function of k in the presence of condensate. An obtained spectrum has a power -3.0 and is close to the one observed in the numerical experiment (power ~-3.1).

## Disorder-driven transition to tubular phase in anisotropic two-dimensional materials

11 November 2022 in 11:30

M.V. Parfenov, V.Yu. Kachorovskii, I.S. Burmistrov

We develop a theory of anomalous elasticity in disordered two-dimensional flexible materials with orthorhombic crystal symmetry. Similar to the clean case, we predict existence of infinitely many flat phases with anisotropic bending rigidity and Young's modulus showing power-law scaling with momentum controlled by a single universal exponent the very same as in the clean isotropic case. With increase of temperature or disorder these flat phases undergo crumpling transition. Remarkably, in contrast to the isotropic materials where crumpling occurs in all spatial directions simultaneously, the anisotropic materials crumple into tubular phase. In distinction to clean case in which crumpling transition happens at unphysically high temperatures, a disorder-induced tubular crumpled phase can exist even at room-temperature conditions. Our results are applied to anisotropic atomic single layers doped by adatoms or disordered by heavy ions bombarding.

## Generalization of Talaska formula for vectrors at internal edges of planar graphs

11 November 2022 in 11:30 (short)

S. Abenda, P.G. Grinevich

The following mathematical construction appears in many problems of mathematical physics including soliton solutions of the KP 2 equation and on-shell amplitude calculations for N=4 supersymmetric Yang-Mills. Consider a planar oriented graph in the upper half-plane with positive weights on edges, satisfying some additional conditions. Let the vectors on the boundary vertices - sources are expressed as sums along all paths from the boundary to the boundary. If the graph has non-trivial cycles, these sums are infinite, but these infinite sums can be expressed as rational expressions with positive denominators using Talaska formula. We show that a generalization of Talaska formula can be written for vectors at interlal edges of the graph.

## Solution of the Lam problem of signatures on planar graphs

11 November 2022 in 11:30 (short)

S. Abenda, P.G. Grinevich

In this work we consider the same graphs as in the previous talk. The vectors at intrernal graphs can be represented either as sums of all paths to the boundary or as solutions of some linear system of equation. This system of eqiations shall inculde some system signs (signature), which is sufficiently non-trivial. Lem proved that such system exists but provided no explicit formula. We suggesed an explicit rule for a signature and proved that, if the graph satisfy some natural additional condition (no dead ends), then the signature is unuque up to a natural gauge transformation.

## Modelirovanie chetyrekhkomponentnoi modeli Pottsa na geksagonal’noi reshetke metodom Vanga-Landau s kontroliruemoi tochnost’yu

21 October 2022 in 11:30 (short)

Численно исследуется критическое поведение четырехкомпонентной модели Поттса на гексагональной решетке. Использован модифицированный метод Ванга-Ландау с контролем точности оценки плотности состояний. Конечномерный анализ полученных результатов подтверждает наличие фазового перехода второго рода с критическими показателями, соответствующими классу универсальности двумерной четырехкомпонентной модели Поттса.
Будет опубликовано в ЖЭТФ, том 162, выпуск 6

## Some comments on the QQqq and QQqqq-quark systems

16 September 2022 in 11:30

Oleg Andreev

I will discuss how compact tetra and pentaquarks could be seen in the QQqq and QQqqq-quark systems.

## Asymmetric higher-harmonic SQUID as a Josephson diode

9 September 2022 in 11:30

Ya.V. Fominov, D.S. Mikhailov

We theoretically investigate asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics. Our main focus is on the «minimal model» with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. The current-voltage characteristic (CVC) turns out to be asymmetric, I(−V) ≠ −I(V). The asymmetry is due to the presence of the second harmonic and depends on the magnetic flux through the interferometer loop, vanishing only at special values of the flux such as integer or half-integer in the units of the flux quantum. The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the simplest manifestations of which is the direction dependence of the critical current. We analyze asymmetry of the overall I(V) shape both in the absence and in the presence of external ac irradiation. In the voltage-source case of external signal, the CVC demonstrates the Shapiro spikes. The integer spikes are asymmetric (manifestation of the JDE) while the half-integer spikes remain symmetric. In the current-source case, the CVC demonstrates the Shapiro steps. The JDE manifests itself in asymmetry of the overall CVC shape, including integer and half-integer steps.
arXiv:2208.10856

## Generalized multifractality in the spin quantum Hall symmetry class with interaction

2 September 2022 in 11:30

I.S. Burmistrov

Scaling of various local observables with a system size at Anderson transition criticality is characterized by a generalized multifractality. We study the generalized multifractality in the spin quantum Hall symmetry class (class C) in the presence of interaction. We employ Finkel'stein nonlinear sigma model and construct the pure scaling derivativeless operators for class C. Within two-loop renormalization group analysis we compute the anomalous dimensions of these pure scaling operators and demonstrate that they are affected by the interaction. We find that the interaction breaks exact symmetry relations between generalized multifractal exponents known for a noninteracting problem.

## Self-consistent equation for torsion arising as a consequence of the Dirac sea quantum fluctuations in external classical electromagnetic and gravitational fields

2 September 2022 in 11:30 (short)

S.N. Vergeles

The quantum fluctuations of the Dirac field in external classical gravitational and electromagnetic fields are studied. A self-consistent equation for torsion is calculated, which is obtained using one-loop fermion diagrams.
Class. Quantum Grav. 39, 155009 (2022); arXiv:2203.03625

## Spectral Flow construction of N = 2 superconformal Calabi-Yau orbifolds

20 May 2022 in 11:30

A.Belavin, V.Belavin and S.Parkhomenko

For each admissible group, we explicitly construct a special set of primary fields of the corresponding orbifold model using the spectral flow winding and the requirement of mutual locality. Then we show that the OPE of the constructed fields is closed. We also show that the mutual locality ensures the modular invariance of the partition function of the resulting orbifold. Using various examples of orbifolds, we construct chiral and antichiral rings and show that they coincide with the cohomology groups of mutually mirrored CY-manifolds.

## Peculiarities of the density of states in SN bilayers

13 May 2022 in 11:30

A. A. Mazanik, Ya. V. Fominov

We study the density of states (DoS) ν(E) in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter Δ0. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with ν(Δ0)=0 as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that ν(Δ0)>0. (iii) Upon further increasing of the inverse proximity effect, ν(E) gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at E0). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.
arXiv:2205.06171

## Affine Yangian of gl(2) and integrable structures of superconformal field theory

29 April 2022 in 11:30

A. Litvinov

We study of integrable structures in superconformal field theory and more general coset CFT’s related to the affine Yangian Y(\hat{\mathfrak{gl}}gl^​(2)). We derive the relation between the RLL and current realizations and prove Bethe anzatz equations for the spectrum of Integrals of Motion.

## On loop corrections to integrable 2D sigma model backgrounds

29 April 2022 in 11:30 (short)

A. Litvinov

We study regularization scheme dependence of β-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the β-function retains only two tensor structures up to certain terms containing ζ_{3}3​. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and λ-deformed SU(2)/U(l) sigma models, for which these terms disappear.

## Folding transformations for q-Painleve equations

8 April 2022 in 11:30

M. Bershtein

Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.
Based on joint work with A. Shchechkin [arXiv:2110.15320]

## Attenuation and inflection of initially planar shock wave generated by femtosecond laser pulse

25 March 2022 in 11:30

Nail Inogamov

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations. During the first stage, the distance traveled by a near-planar wave DSW ≲ RL is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of DSW ∼ RL, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at DSW ≳ RL. It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of DSW ∼ RL. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening. The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

## On the $QQ\bar q\bar q$-Quark Potential in String Models

11 March 2022 in 11:30 (short)

Oleg Andreev

We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system can be thought of mainly as a compact tetraquark. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. Our estimate of the screening length is in the range of lattice QCD. We also make a comparison with the potential of the $QQq$ system. The potentials look very similar at small quark separations but at larger separations they differ. The reason for this is that the flattening of the potentials happens at two well-separated scales as follows from the two different mechanisms: string breaking by light quarks for $QQq$ and string junction annihilation for $QQ\bar q\bar q$. Moreover, a similar construction can also be applied to the $\bar Q\bar Q qq$ system.

## High-frequency transport and zero-sound in an array of SYK quantum dots

28 January 2022 in 11:30

A.V. Lunkin, N/V/ Feigel'man

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T≫TFL. Electric σ(ω,p) and thermal κ(ω,p) conductivities are calculated as functions of frequency and momentum, for arbitrary values of the particle-hole asymmetry parameter E. At low-frequencies ω≪T we find the Lorentz ratio L=κ(0,0)/σ(0,0) to be non-universal and temperature-dependent. At ω≫T the conductivity σ(ω,p) contains a pole with nearly linear dispersion ω≈splnωT reminiscent of the "zero-sound", known for Fermi-liquids.

## Equations of state (EoS), two white spots in EoS: examples from laser ablation in liquid and from laser driven mechanics of deformable solids

21 January 2022 in 11:30

Inogamov N.A.

Example 1. Uncertainties of EoS in the near-critical region. Numerical modeling of ablation into a liquid has been performed. Molecular dynamics and hydrodynamics codes have been applied. Laser radiation passes through a transparent liquid and illuminates a metal target. Absorption and reflection of light from the target takes place. The range of absorbed energies about 1 J/cm2 of interest for technology is considered: below these values few nanoparticles (NPs) are formed per laser pulse, above - optical breakdown of the liquid takes place. A theory has been developed which, using simulation data and thermodynamic information (equations of state of matter), makes it possible to estimate the mass and composition of NPs formed by laser impact.
[1] N. A. Inogamov, V. V. Zhakhovsky, V. A. Khokhlov, Physical processes during laser ablation into a liquid, Pisma v ZhETP, 115(1), 20-27 (2022).

Example 2. Uncertainty of the EoS state associated with elastic-plastic phenomena in solids. It is necessary to describe both elastic characteristics and supercritical fluid at the same time.
Powerful laser exposure causes irreversible changes in the crystal structure of the target. These changes are the basis of laser shock peening (LSP) technologies. The processes determining the thickness of the residual strain layer and related residual stresses are investigated in this work. It is known that the termination of pinning is associated with the attenuation of the laser shock wave. In this work, new information was obtained concerning the transformation of the wave from elastic-plastic to elastic mode of propagation in the case of picosecond impact. The elastic wave is useless for pinning. It turns out that during the transformation, the classical configuration with the plastic jump and the elastic precursor before it disappears. In this case, the leading edge of the expanding plastic layer gradually reduces its speed below the volume speed of sound, smears inside the rarefaction wave and stops. While the elastic system of waves is very important for the modern laser opto-acoustics applications.
[2] N. A. Inogamov, E. A. Perov, V. V. Zakhovsky, V. V. Shepelev, Y. V. Petrov, S. V. Fortova, Laser Shock Wave: Plasticity, Residual Deformation Layer Thickness and Transition from Elastic-Plastic to Elastic Propagation Mode, Pisma v ZhETP, 115(2), 80-88 (2022).

## Vozmozhnosti spinovykh eksperimentov po fundamental’nym diskretnym simmetriyam na kollaidere NICA v Dubne

14 January 2022 in 11:30

N.N. Nikolaev

Будет дан обзор работ, выполненных в рамках гранта РФФИ 18-02-40092 MEGA (И.А. Кооп, А.И. Мильштейн, А.С. Попов, С.Г. Сальников, П.Ю. Шатунов, Ю.М. Шатунов (ИЯФ им. Будкера) + Н.Н. Николаев (ИТФ им. Ландау)). Будут кратко обсуждены оценки односпиновой Р-нечетной асимметрии в полных сечениях взаимодействия поляризованных протонов и дейтронов (уровень эффекта около 10^{-7}), и предложен новый подход к поиску двухспиновой вектор-тензорной асимметрии в протон-дейтронном рассеянии. Исключение систематических фоновых эффектов на требуемом уровне чувствительность достижимо в новом подходе, основанном на Фурье-анализе осциллирующих асимметрий при работе с быстро прецессирующей в горизонтальной плоскости поляризации дейтронов.

## Deformed Virasoro Algebra via Vertex Operators of affine sl(2)

14 January 2022 in 11:30 (short)

M. Bershtein

A new connection between deformed Virasoro algebra and quantum affine sl(2) was found. We give an explicit realization of Virasoro current via vertex operators of sl(2). The same is done for a twisted version of deformed Virasoro algebra. The motivation comes from the geometry of the instanton moduli spaces, algebraically this should be some version of gl(n)-gl(m) duality Based on joint work with R. Gonin

## On optimization problem of array size for modern DFT libraries.

24 December 2021 in 11:30 (short)

A.O. Korotkevich

The problem of optimal array size for modern FFT (DFT) libraries was formulated as a linear integer program. Solution of the linear integer programming problem using standard linear programming libraries (e.g. glpk) is more than order of magnitude faster that brute force approach. Based on this formulation ad-hoc algorithm was developed and implemented which, in turn, gives several order of magnitude acceleration with respect to methods of integer programming.

## On the possibility of a significant increase in the storage time of ultracold neutrons in traps coated with a liquid helium film

24 December 2021 in 11:30

P.D. Grigoriev, A.M. Dyugaev

It is shown that rough inner walls of a trap of ultracold neutrons can be coated with a superfluid helium film much thicker than the depth of penetration of ultracold neutrons into helium. This coating should reduce the rate of loss of ultracold neutrons caused by absorption in the walls of the trap by orders of magnitude. It is also shown that triangular roughness is more efficient than rectangular for the reduction of the rate of loss of ultracold neutrons. Triangular roughness is more easily implemented technically and such diffraction gratings are fabricated industrially.

## Anisotropic superconductivity onset in quasi-two-dimensional conductors

24 December 2021 in 11:30 (short)

P.D. Grigoriev

A possible explanation of the observed anisotropy of the superconducting transition in several quasi-two-dimensional conductors is proposed, based on the assumption (confirmed by experimental data on the angular dependence of magnetoresistance) on the inhomogeneous superconductivity onset in the form of isolated islands with a size greater than the coherence length. The performed numerical and analytical calculations are used to analyze the experimental data in organic metals.

## Differential substitutions for non-Abelian equations of KdV type

17 December 2021 in 11:30 (short)

We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of the Schwarzian KdV equation. The construction method is based on the auxiliary linear problem for KdV, in which the usual spectral parameter is replaced by a non-Abelian one. This makes possible to introduce arbitrary non-Abelian parameters into differential substitutions and equations under study.

## Features of Hamiltonian dynamics in quasiperiodic potentials in the plane

17 December 2021 in 11:30 (short)

I.A. Dynnikov, A.Ya. Maltsev

We consider smooth finite-parametric families of quasiperiodic potentials in the plane and the features of the Hamiltonian dynamics of particles in such potentials. As can be shown, the description of the geometry of the level lines of such potentials makes it possible to naturally divide such potentials into two classes, the first of which is in a sense closer to regular (periodic) potentials, and the second to random potentials. The geometry of the level lines of a potential should, certainly, be reflected in the features of the geometry of the trajectories when moving in such potentials, which really takes place in a certain energy interval. As shown by numerical studies, however, the dynamics of particles in the considered potentials has one more essential feature. The phase dynamic space is divided into areas in which the integrable dynamics takes place, and areas in which the dynamics has chaotic properties. The fraction of the regions corresponding to the integrable dynamics is large at low energy levels and decreases with increasing energy. In the region of nontrivial geometry of the potential level lines, both regimes are usually represented equally clearly, which entails the corresponding features in the description of the dynamics in such potentials. As an example, we present numerical results for families of potentials that often arise in the study of systems of cold atoms in a plane.

## Dispersionless BKP Equation, the Manakov–Santini System and Einstein–Weyl Structures

10 December 2021 in 11:30 (short)

L.V. Bogdanov

We construct a map from solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov–Santini (MS) system. This map defines an Einstein–Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein–Weyl structure corresponding to the MS system. We give a spectral characterisation of reduction in the MS system, which singles out the image of the dBKP equation solutions, and also consider more general reductions of this class. We define the BMS system and extend the map defined above to the map (Miura transformation) of solutions of the BMS system to solutions of the MS system, thus obtaining an Einstein–Weyl structure for the BMS system.

## Matrix extension of multidimensional dispersionless integrable hierarchies

10 December 2021 in 11:30 (short)

L.V. Bogdanov

We consistently develop a recently proposed scheme of matrix extensions of dispersionless integrable systems in the general case of multidimensional hierarchies, concentrating on the case of dimension d⩾4. We present extended Lax pairs, Lax–Sato equations, matrix equations on the background of vector fields, and the dressing scheme. Reductions, the construction of solutions, and connections to geometry are discussed. We separately consider the case of an Abelian extension, for which the Riemann–Hilbert equations of the dressing scheme are explicitly solvable and give an analogue of the Penrose formula in curved space.

## On S-matrix in T ̄T-like perturbed RSOS models

10 December 2021 in 11:30

Daria Shabetnik, Yaroslav Pugai

We give a short introduction to the integrable TT-deformation of QFT by Smirnov-Zamolodchikov. Basic properties of the deformed theories are discussed: factorization, Burgers equation for energy spectrum and exact deformed S-matrix. We study the lattice counterpart of the TT deformation for the case of RSOS(2, 2s+1) models. Starting from the deformed Bethe ansatz equations in thermodynamic limit, we obtain the energies and momenta of the ground and excited states, as well as the deformed breather S-matrix. In the scaling limit the results are in agreement with Smirnov-Zamolodchikov answers.

## Correspondence between the type of the diffraction spectrum on a subwavelength resonant grating and its profile

3 December 2021 in 11:30 (short)

Vergeles S.S., Efremova E.A., Perminov S.V.

We study the resonances in transmission of a subwavelength dielectric lossless structure, periodic in one direction and infinite in the orthogonal. We show that the diffraction type of the grid is determined by the geometric filling factor and the degree of asymmetry of the grid's profile. These two parameters are some linear functions of the complex amplitude of the second spatial Fourier harmonic of the material distribution in the grid. .
[1] Efremova, E. A., Perminov, S. V., & Vergeles, S. S. (2021). Resonance behavior of diffraction on encapsulated guided-mode grating of subwavelength thickness. Photonics and Nanostructures-Fundamentals and Applications, 46, 100953.

## The structure of coherent geostrophic vortices at a finite Rossby number and in the presence of friction on the boundary.

3 December 2021 in 11:30

Vergeles S.S., Parfenyev V.M., Vointsev I.A., Skoba A.O.

The strong rotation makes the turbulent flow quasi-two-dimensional, that leads to the transfer of energy on a large scale. Recent numerical simulations show that under certain conditions, energy accumulates on the largest scales of the system, forming coherent vortex structures known as condensates. We have carried out an analytical description of the interaction of a strong condensate with weak small-scale turbulent pulsations and obtained an equation that makes it possible to determine the radial profile of the azimuthal velocity of a coherent vortex. With a fast external rotation, the velocity profiles of cyclones and anticyclones are identical to each other and are well described by a linear-logarithmic dependence. As the external rotation decreases, this symmetry disappears: the maximum velocity in cyclones is higher, and the position of the maximum is closer to the axis of the vortex in comparison with anticyclones. In addition, our analysis shows that the size of the anticyclone cannot exceed a certain critical value, which depends on the Rossby and Reynolds numbers. The maximum size of cyclones is limited only by the size of the system under the same conditions. Next, we took into account the boundary effects. For typical experimental conditions, the profile of the condensate velocity at sufficiently large distances from the vortex axis is determined by the Ekman linear friction associated with the no-slip conditions at the lower and upper flow boundaries. At the distances, the azimuthal velocity of a coherent vortex does not depend on the distance to the center of the vortex and is determined by the energy balance between the pumping power and friction against the boundaries. We investigate the structure of a coherent vortex in this case and compare the results with the profile of the condensate velocity in two-dimensional systems.
[1] Vladimir Parfenyev and Sergey Vergeles. Influence of Ekman friction on the velocity profile of a coherent vortex in a three-dimensional rotating turbulent flow, Physics of Fluids 33, 115128 (2021).
[2] Parfenyev, V. M., Vointsev, I. A., Skoba, A. O., & Vergeles, S. S. (2021). Velocity profiles of cyclones and anticyclones in a rotating turbulent flow. Physics of Fluids, 33(6), 065117.

## MARANGONY CONVECTION WITHIN ELLIPSOIDAL ISOTROPIC DROPLETS FORMED IN FREE STANDING SMECTIC FILMS

19 November 2021 in 11:30

Elena S. Pikina, M.A. Shishkin, S.A. Pikin and B.I. Ostrovskii

The theoretical study of the Marangoni convection within ellipsoidal isotropic droplets spontaneously generated in free standing smectic films (FSSF) heated above the temperature of the bulk smectic-isotropic transition is conducted. The thermoconvective drops instability is due to constant temperature gradient directed along the normal to the plane of the FSSF. Because the isotropic droplets possess the height of units and tens of microns, the effects of gravity on the convection flows can be neglected. Thus, the thermocapillary effect is solely responsible for the instability development within the drops. The specific feature of the system under consideration is that both drop interfaces are free. Besides this, the isotropic droplets in FSSF have a shape of the oblate spheroids. The solution of the Marangoni convection problem for such a drop is a nontrivial problem. At the beginning we have solved the Marangoni convection problem under approximation of the plane liquid layer. The analytical expression for the Marangoni number in dependence on the wave vector k of in-plane instability at various values of the dimensionless Bio (b) parameter was obtained. Because the Marangoni convection does not depend on orientation of the FSSF with isotropic droplets relative to the direction of the gravitational vector g, the cellular flow can be induced in drops for both directions of thermal gradient across the drop: from bottom to top and from top to bottom. This is valid for isotropic droplets with properties of normal fluid (surface tension is a decreasing function of temperature). The corresponding results were published in the paper: E.S. Pikina, B.I. Ostrovskii, and S.A. Pikin, Eur. Phys. J. E (2021) 44:81 , https://doi.org/10.1140/epje/s10189-021-00082-1.
In continuation of this work we have solved the general problem of the critical Marangoni convection flows within isotropic ellipsoidal drops in FSSF in Boussinesq approximation taking the axial symmetry of the system into consideration. Taking into account the small height of the drops, the gravitational force in Navier–Stokes equation (term with the convective buoyancy force) can be neglected. The series of the linearly independent exact critical solutions for Stokes stream functions in ellipsoidal coordinates (with zero-valued time increment) was determined. Accordingly, the exact solutions for the local distribution of the velocities in the drop in linear approximation over the velocity perturbations were derived. The temperature distribution in the ellipsoidal drops and the surrounding air was determined in the frame of the perturbation theory using the deviation from the initial distribution corresponding to the mechanical equilibrium; it was shown that temperature distribution within the drop corresponds to constant temperature vertical gradient. The corresponding exact solution for the temperature disturbances was derived also in linear approximation over perturbations of the velocity and temperature. In doing so we have used the standard boundary conditions of the equality of the temperatures and the heat fluxes at the drop interface. Further the boundary condition for the equality of the tangential forces at the drop surface with account to the thermocapillary force was written in the ellipsoidal coordinates. This condition can be derived for the given Marangoni number with a certain precision, in dependency on the number of terms considered in the expansion of the solution over the parameters of the critical motions. The boundary condition for the given Marangoni number was determined as a function of the parameter characterizing the ratio of the height and radius of the drop and for the different ratios of the heat conductivity of the liquid crystal and air. The main contributions to the critical thermocapillary motions in the drops for different values of the above parameters were determined. The specific feature of the system under consideration is that due to curvature of the drop interface there is always a temperature gradient along its free surface. Thus, thermocapillary convection in ellipsoidal drops is possible for any arbitrarily small Marangoni numbers – in the frame of the approximation used only the type of the convective motion is varying.

## Jet quenching in small sytems

19 November 2021 in 11:30 (short)

B.G. Zakharov

We discuss recent results on possible jet quenching in collisions of small systems: in $pp$, $pA$ and oxygen-oxygen collisions. Calculations of the radiative and collisional parton energy loss are performed for the temperature dependent running QCD coupling. We use parametrization of $\alpha_s(Q,T)$ which has a plateau around $Q \sim \kappa T$ (it is motivated by the lattice calculation of the effective QCD coupling in the QGP). The parameter $\kappa$ has been fitted to the LHC data on the nuclear modification factor $R_{AA}$ in heavy ion collisions. Using the optimal $\kappa$ we perform calculations of $R_{pp}$, $R_{pPb}$, and $R_{AA}$ and $v_2$ for O+O collisions. We find that predictions for $R_{OO}$ may differ substantially for scenarios with and without mini-QGP formation in $pp$ collisions. We show that the available data on $R_{pPb}$ may be consistent with the QGP formation in $pp$ and $pPb$ collisions. However, a scenario with the QGP formation only in pPb collisions is excluded.

## Radiative $p_{\perp}$-broadening of fast partons in an expanding quark-gluon plasma

19 November 2021 in 11:30 (short)

B.G. Zakharov

We study contribution of radiative processes to $p_{\perp}$-broadening of fast partons in an expanding quark-gluon plasma. It is shown that the radiative correction to $\langle p_{\perp}^2\rangle$ for the QGP produced in $AA$-collisions at RHIC and LHC may be negative, and comparable in absolute value with the non-radiative contribution. We have found that the QGP expansion enhances the radiative suppression of $p_\perp$-broadening as compared to the static medium. Our results show that the radiative contribution to $p_{\perp}$-broadening can make the total $\langle p_{\perp}^2\rangle$ very small for heavy ion collisions at the RHIC and LHC energies. This can explain the absence of a considerable jet acoplanarity in hadron-jet events at RHIC and LHC.

## A note on the vacuum structure of lattice Euclidean quantum gravity: “birth” of macroscopic space-time and PT-symmetry breaking

22 October 2021 in 11:30 (short)

S.N. Vergeles

It is shown that the ground state or vacuum of the lattice quantum gravity is significantly different from the ground states of the well-known vacua in QED, QCD, et cetera. In the case of the lattice quantum gravity, the long-wavelength scale vacuum structure is similar to that in QED, moreover the quantum fluctuations of gravitational degrees of freedom are very reduced in comparison with the situation in QED. But the small scale (of the order of the lattice scale) vacuum structure in gravity is significantly different from that in the long-wavelength scales: the fluctuation values of geometrical degrees of freedom (tetrads) are commensurable with theirs most probable values. It is also shown that the macroscopic Universe can exist only in the presence of fermion fields. In this case, spontaneous breaking of the PT symmetry occurs.

## Picosecond laser action on iron films: elastic, plastic and polymorphic transformations

22 October 2021 in 11:30 (short)

Khokhlov V. A., Ashitkov S. I., Inogamov N. A., Komarov P. S., Mursov S. A., Struleva E. V., Zhakhovsky V. V.

The results of experimental studies of laser shock waves initiated by a picosecond pulse in iron are presented. The experimental data were processed and analyzed using theoretical approaches and numerical modeling. To elucidate the kinetics of polymorphic transformation on picosecond time scales, the method of inverse analysis of the free surface velocity was used for the first time. Validation of the method was carried out using the results of hydrodynamic and molecular dynamic modeling with direct extraction of mechanical stresses and deformations.

## Diffraction on a Microbubble and the Morphology of the Silicon Surface Irradiated through Glycerol by a Pair of Femtosecond Laser Pulses

22 October 2021 in 11:30

Inogamov, N. A.; Romashevskiy, S. A.; Ignatov, A. I.; Zhakhovsky, V. V.; Khokhlov, V. A.; Eganova, E. M.; E. A. Pershina & Ashitkov, S. I.

The effect of two successive laser pulses on silicon placed in glycerol has been studied experimentally and numerically with electromagnetic, hydrodynamic, and atomistic simulation programs. It has been shown that a microbubble in the liquid is formed on the surface after the first pulse; then, the second pulse whose width is comparable with the diameter of the microbubble is diffracted on this microbubble. The calculated diffraction pattern and light intensity distribution on the silicon surface indicate that the maximum intensity at the diffraction peaks can be noticeably higher than the intensity on the axis of the incident Gaussian beam. An increase in the intensity concentrated in one bright narrow ring around the microbubble results in the formation of a characteristic groove surrounded by ridges on silicon. The molecular dynamics simulation has shown that intense heating at the diffraction peak is responsible for the melting and displacement of the melt from the center of heating. This leads to the formation of grooves with ridges having a profile similar to that measured in the experiment.

## Poisson brackets of hydrodynamic type and their generalizations

15 October 2021 in 11:30 (short)

A.Ya. Maltsev, S.P. Novikov

We consider Hamiltonian structures of hydrodynamic type and some of their generalizations. In particular, we discuss the questions concerning the structure and special forms of the corresponding Poisson brackets and the connection of such structures with the theory of integration of systems of hydrodynamic type. (JETP, 132(4), 645-657 (2021))

## String breaking in a cold wind as seen by string models

8 October 2021 in 11:30 (short)

Oleg Andreev

We model a heavy quark-antiquark pair in a color singlet state moving through a cold medium and explore the consequences of temperature and velocity on string breaking. We show that the string breaking distance slowly varies with temperature and velocity away from the critical line but could fall near it.
arXiv:2106.14716

## Quantum mechanics of radiofrequency-driven coherent beam oscillations in storage rings

8 October 2021 in 11:30

J. Slim, N.N. Nikolaev, F. Rathmann and A. Wirzba

We report the first ever treatment of the quantum regime of the radiofrequency driven collective betatron oscillations in storage rings. Remarkably, the collective oscillation amplitude is described by one and the same formula from the classical large amplitudes down to the deep quantum regime way below the Heisenberg limit for single parricle oscillations. The results are of relevance to the precision search for the EDM of protons.

## Squared eigenfunction decomposition near Akhmediev breather

24 September 2021 in 11:30 (short)

P.G. Grinevich, P.M. Santini

The Akhmediev breather and its M-soliton generalization, are exact solutions of the focusing NLS equation periodic in space and exponentially localized in time over the constant unstable background; they describe the appearance of M unstable nonlinear modes and their interaction. It is important to establish the stability properties of these solutions under perturbations, to understand if they appear in nature, and in which form. Recently we found out that in contrast with the common believe in the literature these in linear approximations of perturbation theory these solutions are exponentially unstable and constructed the unstable modes explicitly in terms of derivatives of the squared eigenfunctions with respect to the spectral parameter by direct matching of coefficients. In the recent talk we explain how to derive these solutions using the technique developed by Krichever for the KP equation.

## Mean-field interactions in evolutionary spatial games

24 September 2021 in 11:30 (short)

L. Shchur

We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent operates based on local information from its neighbors and non-local information via the mean-field coupling. We simulate the model and construct the steady-state phase diagram, which shows significant new features due to the mean-field term: while for the game of Nowak and May, steady states are characterized by a constant mean density of cooperators, the mean-field game contains steady states with a continuous dependence of the density on the payoff parameter. Moreover, the mean-field term changes the nature of transitions from discontinuous jumps in the steady-state density to jumps in the first derivative. The main effects are observed for stationary steady states, which are parametrically close to chaotic states: the mean-field coupling drives such stationary states into spatial chaos. Our approach can be readily generalized to a broad class of spatial evolutionary games with deterministic and stochastic decision rules.
Based on paper accepted to Physical Review Research, with D. Antonov and E. Burovski, arXiv:2107.11088

## Algorithm for replica redistribution in implementation of the population annealing method on a hybrid supercomputer architecture

24 September 2021 in 11:30 (short)

L. Shchur

A population annealing method is a promising approach for large-scale simulations because it is potentially scalable on any parallel architecture. We present an implementation of the algorithm on a hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible by efficiently redistributing replicas. We provide details of testing on hardware based on the Intel Skylake/Nvidia V100 running more than two million replicas of the Ising model sample in parallel. The results are quite encouraging because the acceleration grows toward the perfect line as the complexity of the simulated system increases.
Based on the paper with A. Russkov and R Chulkevich, Computer Physics Communications, 261 (2021) 107786

## Explicit construction of N = 2 superconformal orbifolds

3 September 2021 in 11:30

A. Belavin, S. Parkhomenko

Following Gepner's approach, we propose a construction of models of tensor product orbifolds of Minimal models of two-dimensional Field Theory with N = 2 superconformal symmetry. To build models that satisfy the requirements of modular invariance, our construction uses a spectral flux transformation. We demonstrate this construction with a specific example and show that its application ensures the modular invariance of the partition function simultaneously with the mutual locality of the fields of the theory under consideration.

## Anomalous elasticity of anisotropic flexible two-dimensional materials

3 September 2021 in 11:30

Burmistrov I.S.

We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. We show that in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale ~10 nm, these materials possess flat phases with anisotropic bending rigidity and Young's modulus. Remarkably, the problem has continuous hidden symmetry, which leads to formation of the line of fixed points. We demonstrate that due to this symmetry the power law scaling with momentum is controlled by the single universal exponent (the same along the whole line). We demonstrate that these anisotropic flat phases are uniquely labeled by the ratio of absolute Poisson's ratios. We apply our theory to monolayer black phosphorus (phosphorene).

## Superconducting phases and the second Josephson harmonic in tunnel junctions between diffusive superconductors

18 June 2021 in 12:30

A.S. Osin, Ya.V. Fominov

We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions. The talk is based on the paper [1].

[1] A.S. Osin and Ya.V. Fominov, arXiv:2105.05786

## Relation between multifractality and entanglement for nonergodic extended states

18 June 2021 in 11:30

Ivan M. Khaymovich (MPIKS, Dresden)

The multifractality provides a way of ergodicity breaking in term of chaotization and equipartitioning over degrees of freedom. On the other hand, in quantum information theory it is the entanglement entropy which represents the main measure of ergodicity and thermalization. In this talk I will represent an exact relation between the above measures, showing that the fractal dimension of the non-ergodic wave function puts an upper bound on its entanglement entropy [A]. I will also provide a couple of explicit examples demonstrating that the entanglement entropy may reach its ergodic (Page) value when the wave function is still highly non-ergodic and occupies a zero fraction of the total Hilbert space. If time permits I will briefly discuss some other possible deviations from ergodicity relevant for the chaotic many-body systems [B-E].

[A] G. De Tomasi, I. M. K., “Multifractality meets entanglement: relation for non-ergodic extended states”, Phys. Rev. Lett. 124, 200602 (2020) [arXiv:2001.03173]
[B] I. M. K., M. Haque, and P. McClarty, “Eigenstate Thermalization, Random Matrix Theory and Behemoths”, Phys. Rev. Lett. 122, 070601 (2019) [arXiv:1806.09631].
[C] M. Haque, P. A. McClarty, I. M. K. , “Entanglement of mid-spectrum eigenstates of chaotic many-body systems—deviation from random ensembles.” [arXiv:2008.12782].
[D] A. Bäcker, I. M. K., M. Haque,, “Multifractal dimensions for chaotic quantum maps and many-body systems”, Phys. Rev. E 100, 032117 (2019) [arxiv:1905.03099].
[E] G. De Tomasi, I. M. K. , "Ergodic Entanglement of many-body multifractal states in quadratic Hamiltonians", in preparation

## Interaction of a Neel-type skyrmion and a superconducting vortex

11 June 2021 in 11:30

E.S. Andriyahina, I.S. Burmistrov

Superconductor-ferromagnet heterostructures hosting vortices and skyrmions are new area of an interplay between superconductivity and magnetism. We study [1] an interaction of a Neel-type skyrmion and a Pearl vortex in thin heterostructures due to stray fields. Surprisingly, we find that it can be energetically favorable for the Pearl vortex to be situated at some nonzero distance from the center of the Neel-type skyrmion. The presence of a vortex-antivortex pair is found to result in increase of the skyrmion radius. Our theory predicts that a spontaneous generation of a vortex-anti-vortex pair is possible under some conditions in the presence of a Neel-type skyrmion that is in agreement with recent experiment [2].
[1] E.S. Andriyakhina. and I.S. Burmistrov “Interaction of a Néel–type skyrmion and a superconducting vortex” // arXiv: https://arxiv.org/abs/2102.05434.
[2] A.P. Petrović et al. “Skyrmion-(Anti)vortex coupling in a chiral magnet-superconductor heterostructure” // Phys.Rev. Lett.126, 117205 (2021).

## Vortex structure in a clean superconductor in the vicinity of a planar defect

11 June 2021 in 11:30

U.E. Khodaeva, M.A. Skvortsov

We investigate the structure of the quasiparticle states localized in a superconducting vortex core in the vicinity of a planar defect. It is shown that even a highly transparent defect leads to a significant modification of the excitation spectrum, with the opening of a minigap at the Fermi energy. The magnitude of the minigap exceeds the mean level spacing for a clean vortex already for small values of the reflection coefficient off the defect. It is maximal for the vortex sitting right at the defect, decreases with increasing the distance from the defect and closes at some point. We then generalize the problem for various configurations of several linear defects (periodic structures, two crossing lines, stars). Though the minigap remains, a strong commensurability effect is observed. For two crossing linear defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational number.

## Dynamical phases in Rosenzweig-Porter model with a ’multifractal’ distribution of hopping

4 June 2021 in 11:30

We consider a Rosenzweig-Porter (RP) random matrix model with broad distribution of off-diagonal matrix elements which emerge as a model equivalent to the Anderson model on random regular graph. In this work we study the survival probability of a quantum particle with wave function initially localized on one site described by such type of model and show that the strongly non-Gaussian, broad distribution of hopping leads to the stretch-exponential decay of survival probability with time. We show that the ergodic phase with the stretch-exponential behavior of survival probability emerges in this model exactly where on a finite Bethe lattice there is a multifractal phase and relate the stretch exponent $\kappa$ with the kernel \epsilon_{\beta} of the transfer-matrix equation on a Bethe lattice.
We also consider the extension of this RP model relaxing the symmetry inherited from the Bethe lattice and find lines of phase transitions from the exponential to the stretch exponential behavior of survival probability.

## Microwave response of a chiral Majorana interferometer

14 May 2021 in 11:30

Alexander Shnirman (Karlsruhe Institute of Technology)

We consider an interferometer based on artificially induced topological superconductivity and chiral 1D Majorana fermions. The (non-topological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency dependent impedance between the island and the earth. Namely, charging and discharging of the island is controlled by the time-delayed interference of chiral Majorana excitations in both normal and Andreev channels. We argue that microwave measurements provide a direct way to observe the physics of 1D chiral Majorana modes.

## Two-impurity scattering in quasi-one-dimensional systems

14 May 2021 in 11:30

A.S. Ioselevich, N.S. Peshcherenko

In a quasi-one-dimensional system (a tube) with low concentration of defects $n$ the resistivity $\rho$ has peaks (van-Hove singularities) as a function of Fermi-energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap ($\rho_{\min}\propto n^2$) is dominated by scattering at rare twin-pairs'' of close defects, while scattering at solitary defects is suppressed. This effect is characteristic for multi-channel systems, it can not be observed in strictly one-dimensional one.

## Conductivity and thermoelectric coefficients of doped SrTiO3 at high temperatures

30 April 2021 in 11:30

Kh. Nazaryan, M.V. Feigelman

We developed a theory of electric and thermoelectric conductivity of lightly doped SrTiO3 in the non-degenerate region k_B T ≥ E_F , assuming that the major source of electron scattering is their interaction with soft transverse optical phonons present due to proximity to ferroelectric transition. We have used kinetic equation approach within relation-time approximation and we have determined energy-dependent transport relaxation time τ (E) by the iterative procedure. Using electron effective mass m and electron-transverse phonon coupling constant λ as two fitting parameters, we are able to describe quantitatively a large set of the measured temperature dependences of resistivity R(T ) and Seebeck coefficient S(T ) for a broad range of electron densities studied experimentally in recent paper by K.Behnia and his colleagues. In addition, we calculated Nernst ratio in the linear approximation over weak magnetic field in the same temperature range.

## Multiple Equilibria and Resilience in Large Complex Systems: beyond May-Wigner model

9 April 2021 in 11:30

Yan Fyodorov

We consider two different models of randomly coupled N>>1 autonomous differential equationswith the aim of counting fixed points (aka equilibria), and classifying them by their ''instability index'', i.e. the number of unstable directions. In the first model, characterized by both translational and rotational statistical symmetry of the vector field, we estimate the probability of an equilibrium to have a given index in a phase with exponentially many equilibria. In the second model, characterized by only rotational statistical symmetry around a chosen stable equilibrium, we find a characteristic distance beyond which the multitude of equilibria prevents a trajectory to go towards the stable equilibrium. This may shed light on ''resilience'' mechanisms of complex ecosystems.

## Six-waves kinetic equation and its applicability to quintic NLSE

9 April 2021 in 11:30 (short)

J. Banks, T. Buckmaster, A.O. Korotkevich, G. Kovacic, J. Shatah

We consider kinetic equation for quintic-NLSE, corresponding to 6-wave nonlinear waves interaction. Kinetic equation for the periodic boundary conditions was derived. We propose conditions on equation parameters which guarantee reasonably accurate description of the wave field by wave kinetic equation. Direct numerical simulations in both dynamical equation and wave kinetic equation frameworks demonstrate acceptable correspondence between these significantly different models when proposed conditions for parameters are satisfied.

## On coincidence of periods of the Berglund–Hübsch–Krawitz (BHK) multiple mirrors

2 April 2021 in 11:30 (short)

A.A. Belavin

We consider the multiple Calaby-Yau (CY) mirror phenomenon which appears in Berglund-Hübsch-Krawitz (BHK) mirror symmetry. We show that the periods of the holomor phic nonvanishing form of different Calabi-Yau orbifolds, which are BHK mirrors of the the same CY family, coincide.
Alexander Belavin, Vladimir Belavin, Gleb Koshevoy, "Periods of Berglund–Hübsch–Krawitz mirrors", arXiv: hep-th-2012.03320 ; "Periods of the multiple Berglund–Hübsch–Krawitz mirrors", Letters in Mathematical Physics, 111, 93 (2021).

## On matrix Painlev\'e II equations

26 March 2021 in 11:30 (short)

The Painlev\'e--Kovalevskaya test is applied to find three matrix versions of the Painlev\'e II equation. All these equations are interpreted as group-invariant reductions of integrable matrix evolution equations, which makes it possible to construct isomonodromic Lax pairs for them.

## Order parameter distribution in strongly disordered superconductors: analytical theory

12 March 2021 in 11:30

A. V. Khvalyuk, M. V. Feigel'man

We analyze the spatial distribution of the order parameter \Delta(r) in strongly disordered superconductors close to Superconductor-Insulator Transition. The analysis is based on a model of a superconductor on a locally loopless lattice with a pseudogap. We derive and solve a set of equations for the local distribution function P(\Delta) at zero temperature. The results are applicable both in the region of relatively small disorder corresponding to a Gaussian profile of P(\Delta) and in the region of strong fluctuation. The analytical results are in excellent agreement with the direct numerical solution of the self-consistency equations.

## Tail states and unusual localization transition in low-dimensional Anderson model with power-law hopping

12 March 2021 in 11:30

K.S. Tikhonov, A.S. Ioselevich and M.V. Feigel'man

We study determininstic power-law quantum hopping model local Gaussian disorder in low dimensions d = 1, 2 under the condition d < β < 3d/2. We demonstrate unusual combination of exponentially decreasing density of the ”tail states” and localization-delocalization transition (as function of disorder strength w) pertinent to a small (vanishing in thermodynamic limit) fraction of eigenstates. In a broad range of parameters density of states ν(E) decays into the tail region E < 0 as simple exponential. We develop simple analytic theory which describes E0 dependence on power-law exponent β, dimensionality d and disorder strength W , and compare its predictions with exact diagonalization results. At low energies within the bare ”conduction band”, all eigenstates are localized due to strong quantum interference at d = 1, 2; however localization length grows fast with energy decrease, contrary to the case of usual Schrodinger equation with local disorder.

## Multifractally-enhanced superconductivity in thin films

26 February 2021 in 11:30

I.S. Burmistrov

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

## Remarks on Static Three-Quark Potentials and String Breaking

12 February 2021 in 11:30 (short)

Oleg Andreev

Making use of the gauge/string duality, it is possible to study some aspects of the string breaking phenomenon in the three quark system. Our results point out that the string breaking distance is not universal and depends on quark geometry. The estimates of the ratio of the string breaking distance in the three quark system to that in the quark-antiquark system would range approximately from 2/3 to 1. In addition, it is shown that there are special geometries which allow more than one breaking distance.

## Ground state of a quantum particle in a potential field. Modeling of potentials by the inverse problem method (dedicated to the memory of A. Shabat)

18 December 2020 in 11:30

Alexander Dyugaev, Pavel Grigoriev

The solution of the Schrödinger equation for the ground state of a particle in a potential field is investigated. Since the wave functions of the ground state have no nodes, it turns out to be possible to unambiguously determine potentials of different types. It turned out that for a wide range of model potentials the ground state energy is zero. Moreover, the zero level may be the only level at the edge of the continuous spectrum. The crater-type potentials, which have a monotonic dependence on coordinates, are considered for the case of one, two and three dimensions. In the one-dimensional case, of interest are potentials of the "instanton" type with two equilibrium points of the particle. For the Coulomb potential, the ground state energy is stable to its screening, both at large and small distances. Two-soliton solutions of the nonlinear Schrödinger equation are found. The effectiveness of the proposed "inverse problem method" for investigating the solutions of differential equations is argued.
We found a wide class of potentials for which the energy of the ground state is stationary during the translations of wave function for the dimension d = 1,2,3. For dimension d = 1, these functions are known from the theory of nonlinear equations. Examples of nonlinear equations with zero ground state energy are given. Functions localized on a sphere and the crater-like potentials are investigated.

## Order parameter and heat capacity of superconducting granules

18 December 2020 in 11:30 (short)

Alexander Dyugaev, Pavel Grigoriev

The thermodynamic properties of superconducting granules with a small parameter $\delta = \varepsilon_0 / Tc$ are determined, where $\varepsilon_0$ is the distance between the levels of dimensional quantization, $Tc$ is the temperature of the transition to the superconducting state of the bulk sample. It is shown that the order parameter $\Delta (T)$ does not vanish at $T > Tc$ and even passes through a minimum at $T \approx eTc$; where $\Delta (eTc) / \Delta (0) \approx \delta ^{1/2}$, and at the transition point $\Delta (Tc) / \Delta (0) \approx \delta ^ {1/4 }$. The parameter $\Delta (T) \gg \varepsilon_0$ in a wide temperature range $T> Tc$, for example, $\Delta (eTc) / \varepsilon_0 \sim \delta ^ {- 1/2}$.
The temperature dependence of the excess heat capacity of granules $\Delta C = [C_S (T) -C_N (T)] / C_N (Tc)$ is determined, where $C_S$ and $C_N$ are the heat capacities of the superconducting and normal phases. At low T, the heat capacity of the granules does not depend on their size. At $T \rightarrow Tc \; \; \Delta C (Tc) = A (1-2 / \pi)$, where $A$ is the jump in the heat capacity of the bulk sample. In the region $T> Tc$, $\Delta C (T)$ depends only on the parameter $z = ln (T/Tc) / \delta^{1/2}$; for $z> 1$ $\Delta C = 3/ (2\pi ^2 z^2)$. The slow logarithmic dependence $\Delta C (T)$ can be experimentally observed at $T \sim 2Tc$.

## Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background

11 December 2020 in 11:30 (short)

L.V. Bogdanov

We obtain a dispersionless integrable system describing a local form of a general three-dimensional Einstein–Weyl geometry with a Euclidean (positive) signature, construct its matrix extension, and show that it leads to the Bogomolny equations for a non-Abelian monopole on an Einstein–Weyl background. We also consider the corresponding dispersionless integrable hierarchy, its matrix extension, and the dressing scheme.

## Collective nuclear vibrations and initial state shape fluctuations in central Pb+Pb collisions: resolving the $v_2$ to $v_3$ puzzle

11 December 2020 in 11:30 (short)

B.G. Zakharov

We have studied, for the first time, the influence of the collective quantum effects in the nuclear wave functions on the azimuthal anisotropy coefficients $\epsilon_{2,3}$ for the initial quark-gluon plasma fireball in the central Pb+Pb collisions at the LHC energies. With the help of the energy weighted sum rule we demonstrate that the classical treatment with the Woods-Saxon nuclear density overestimates the mean square quadrupole moment of the $^{208}$Pb nucleus by a factor of $\sim 2.2$. The Monte-Carlo Glauber simulation of the central Pb+Pb collisions accounting for the restriction on the quadrupole moment leads to a substantial suppression of the ratio $\epsilon_2/\epsilon_3$ which allows to resolve the $v_2$-to-$v_3$ puzzle.
B.G. Zakharov, Collective nuclear vibrations and initial state shape fluctuations in central Pb + Pb collisions: resolving the $v_2$ to $v_3$ puzzle, Письма в ЖЭТФ, 112 (7), 435-436 (2020)

## Jet quenching in heavy ion collisions at RHIC and LHC energies

11 December 2020 in 11:30

B.G. Zakharov

We present results of a detailed global analysis of experimental data on the nuclear modification factor $R_{AA}$ and the flow coefficient $v_2$ for light hadrons from RHIC for 0.2 TeV Au+Au collisions and from LHC for 2.76 and 5.02 TeV Pb+Pb, and 5.44 TeV Xe+Xe collisions. We perform calculations within the light-cone path integral approach to induced gluon emission. We use running $\alpha_s$ which is frozen at low momenta at some value $\alpha_{s}^{fr}$. We find that the RHIC data support somewhat larger value of $\alpha_{s}^{fr}$. For the $\chi^2$ optimized values of $\alpha_{s}^{fr}$, the theoretical predictions are in reasonable agreement with data on $R_{AA}$ and $v_2$. Calculations made for different formation times and life-times of the QGP show that jet quenching at the RHIC and LHC energies is only weakly sensitive to the initial and final stages of the QCD matter evolution. One of the reasons for difference between the optimal $\alpha_s$ for RHIC and LHC is a stronger thermal suppression of the QCD coupling in the hotter quark-gluon plasma at the LHC energies. To clarify the situation we also perform calculations with temperature dependent running $\alpha_s$. Our results show that the $T$-dependent QCD coupling largely eliminates the difference between the optimal values of $\alpha_s$ for the RHIC and LHC energies. It may be viewed as the first direct evidence of the increase of the thermal suppression of $\alpha_s$ with rising temperature.

## Unstable modes for linearization of NLS near Akhmediev breather

11 December 2020 in 11:30 (short)

P. G. Grinevich, P.M. Santini

The literature contains the statement that Akhmediev breather is stable due to "saturation of nonlinearity". The argument supporting this statement is that the solutions of linearized problems are expanded in terms of squared eigenfunctions, and non of them grows in time. We show this argument is wrong, because of the double point in the spectral problem the squared eigenfunctions expansion includes derivatives in the spectral parameter. We also explicitly calculate the "missing modes".

## Quantum breakdown of superconductivity in low-dimensional materials

4 December 2020 in 11:30

M.V. Feigel'man

A brief overview of the main results of the experimental and theoretical works of the last ~ 10 years on quantum phase superconductor-insulator and superconductor-metal transitions will be done. In addition, it is supposed to provide some list of the main unsolved problems in this area.
B. Sacépé, M. Feigel'man, T.M. Klapwijk, Quantum breakdown of superconductivity in low-dimensional materials, Nature Physics 16, 734-746 (2020); arXiv:2007.15870

## Reconstructions of the electron dynamics in magnetic field and the geometry of complex Fermi surfaces

20 November 2020 in 11:30 (short)

A.Ya. Maltsev

We consider the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of closed extremal trajectories of a special form, closely related to geometry and topology of the Fermi surface. The study of oscillation phenomena on such trajectories allows, in particular, to propose a relatively simple method for refining the parameters of the dispersion relation in metals with complex Fermi surfaces.

## Moutard transformation for the two-dimensional heat conductivity operator

13 November 2020 in 11:30 (short)

P. G. Grinevich, R. G. Novikov

We calculate the Moutard transformations for the two-dimensional heat conductivity operator. These transformations act simultaneously at the potentials and at the eigenfunctions. generally existence of Moutard transformations means integrability of the problem. Historically the Darboux transformations were obtained as one-dimensional reductions of Moutard transformations.

## Creation and annihilation of point-potentials using Moutard-type transform in spectral variable

13 November 2020 in 11:30 (short)

P. G. Grinevich, R. G. Novikov

We continue to study the fixed-energy inverse spectral problem for the two-dimensional Schodinger operator at a fixed negative energy above the ground state. In 1988 P.G. Grinevich and S.P. Novikov showed that this spectral problem contains singular contours resulting in very serious analytic difficulties. Recently P.G. Grinevich and R.G. Novikov showed that locally such singularities can be locally removed or added by applying the Moutard transformation. In the present paper we construct a global Moutard transformation in the simplest case, and we show that it adds or removes point potentials.

## Superconductivity Suppression in Disordered Films: Interplay of Two-dimensional Diffusion and Three-dimensional Ballistics

6 November 2020 in 11:30

D.S. Antonenko, M.A. Skvortsov

Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift $\delta T_c/T_{c0} \sim - 1/k_Fl$, where $k_F$ is the Fermi momentum and $l$ is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of $T_c$ suppression with decreasing the film thickness, this effect is caused by the proximity to the three-dimensional Anderson localization threshold and is controlled by the parameter $k_Fl$ rather than the sheet resistance of the film.
D.S. Antonenko, M.A Skvortsov,. JETP Lett. (2020). https://doi.org/10.1134/S0021364020190017

## Numerical investigation of stability of Stokes waves.

6 November 2020 in 11:30

A.O. Korotkevich, S.A. Dyachenko, P.M. Lushnikov, and A.A. Semenova.

We will consider one of the first finite amplitude, meaning inherently nonlinear, solutions for waves on the surface of the fluid, namely, Stokes waves. Linear stability of waves, which were obtained with high precision in our previous works, is investigated. We linearize Dyachenko equations with respect to small perturbations of Stokes waves for incompressible fluid of infinite depth. Resulting equations are reformulated as an eigenvalue problem for a nonlocal linear operator, which is solved on inhomogeneous grid using Arnoldi algorithm with shift-and-invert preconditioner. The first three branches of instability are demonstrated and predictions of the system behavior for higher nonlinearity Stokes waves are proposed.

## Painlev\'e type reductions in the non-Abelian Volterra lattices

30 October 2020 in 11:30 (short)

The Volterra lattice admits two non-Abelian generalizations that preserve the integrability property. For each of them, the stationary equation for non-autonomous symmetries defines a constraint that is consistent with the lattice and leads to Painlev\'e-type equations. In the case of symmetries of low order, including the scaling and master-symmetry, this constraint can be reduced to second order equations. This gives rise to two non-Abelian generalizations for the discrete Painlev\'e equations dP$_1$ and dP$_{34}$ and for the continuous Painlev\'e equations P$_3$, P$_4$ and P$_5$.

## The effect of superconducting fluctuations on the ac conductivity of a 2D electron system in the diffusive regime

23 October 2020 in 11:30 (short)

I.S. Burmistrov

We report a complete analytical expression for the one-loop correction to the ac conductivity $\sigma(\omega)$ of a disordered two-dimensional electron system in the diffusive regime. The obtained expression includes the weak localization and Altshuler–Aronov corrections as well as the corrections due to superconducting fluctuations above superconducting transition temperature. The derived expression has no divergency in the static limit, $\omega\to 0$ , in agreement with general expectations for the normal state conductivity of a disordered electron system. The results are published in I.S. Burmistrov, Ann. Phys. 418, 168201 (2020).

## Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid

16 October 2020 in 11:30

Pavel Nosov, Igor Burmistrov, Srinivas Raghu

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. We instead start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

## Spectroscopic evidence for strong correlations between local resistance and superconducting gap in ultrathin NbN films

16 October 2020 in 11:30 (short)

M.A. Skvortsov and M.V. Feigel'man

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap Δ and of the critical temperature Tc, the ratio Δ/kBTc remaining roughly constant. In addition, in most films, an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature Tc and the energy gap Δ starts decoupling from Tc. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of an NbN film with scanning tunneling spectroscopy (STS), we show that the inhomogeneous spatial distribution of Δ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modeling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of Δ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.

## Critical behavior at the localization transition on random regular graphs

9 October 2020 in 11:30

Konstantin Tikhonov

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. As a first step, we carry out a precise determination of the critical disorder. After this, we determine the dependence of the correlation volume on disorder on the delocalized side of the transition by means of population dynamics. The asymptotic critical behavior is found to be in agreement with analytical prediction based on the stability analysis of the symmetry-broken solution near criticality.

## Conductivity of superconductors in the flux flow regime

9 October 2020 in 11:30

M. Smith, A.V. Andreev, M.V. Feigel'man, and B.Z.Spivak

We develop a theory of conductivity of type-II superconductors in the flux flow regime taking into account random spatial fluctuations of the system parameters, such as the gap magnitude Δ(r) and the diffusion coefficient D(r). We find a contribution to the conductivity that is proportional to the inelastic relaxation time τin, which is much longer than the elastic relaxation time. This new contribution is due to Debye-type relaxation, and it can be much larger than the conventional flux flow conductivity due to Bardeen and Stephen. The new contribution is expected to dominate in clean superconductors at low temperatures and in magnetic fields much smaller than Hc2.

## Coalescence of isotropic droplets in overheated free standing smectic films

2 October 2020 in 11:30

Elena S. Pikina, Boris I. Ostrovskii and Sergey A. Pikin

A theoretical study of the interaction and coalescence of isotropic droplets in overheated free-standing smectic films (FSSF) is presented. Experimentally it is clear that merging of such droplets is extremely rare. On the basis of the general thermodynamic approach to the stability of FSSF, we determined the energy gains and losses involved in the coalescence process. The main contributions to the critical work of drop coalescence are due to the gain related to the decrease of the surface energy of the merging drops, which is opposed by the entropic repulsions of elementary steps at the smectic interface between them. To quantify the evolution of the merging drops, we use a simple geometrical model in which the volume of the smectic material, rearranged in the process of coalescence, is described by an asymmetrical pyramid at the intersection of two drops. In this way, the critical work for drop coalescence and the corresponding energy barrier have been calculated. The probability of the thermal activation of the coalescence process was found to be negligibly small, indicating that droplet merging can be initiated by only an external stimulus. The dynamics of drop merging was calculated by equating the capillary force driving the coalescence, and the Stokes viscous force slowing it down. For the latter, an approximation of moving oblate spheroids permitting exact calculations was used. The time evolution of the height of the neck between the coalescing drops and that of their lateral size are in good agreement with experiments.

E.S. Pikina, B.I. Ostrovskii, S.A. Pikin, Coalescence of isotropic droplets in overheated free standing smectic films, Soft Matter, 16(19), 4591-4606 (2020)

## Zeros of Riemann’s Zeta Functions in the Line z=1/2+it0

25 September 2020 in 11:30

Yu.N. Ovchinnikov

Investigation of Josephson effect, current flow in narrow superconducting stripes, dynamical states in superconductors lead to the necessity to deal with an important phenomenon: phase slip events. The study of the distribution of zeros for Riemann's Zeta function also requires an analisis of the same phenomenon.
It was found that, in addition to trivial zeros in points ($z = -2N, N = 1, 2, ...$, natural numbers), the Riemann’s zeta function $\zeta(z)$ has zeros only on the line {$z = 1/2 + i t_0$, $t_0$ is real}. All zeros are numerated, and for each number, N, the positions of the non-overlap intervals with one zero inside are found. The simple equation for the determination of centers of intervals is obtained. The analytical function $\eta(z)$), leading to the possibility fix the zeros of the zeta function $\zeta(z)$, was estimated. To perform the analysis, the well-known phenomenon, phase-slip events, is used. This phenomenon is the key ingredient for the investigation of dynamical processes in solid-state physics, for example, if we are trying to solve the TDGLE (time-dependent Ginzburg-Landau equation).
J. Supercond. Novel Magn., 32(11), 3363-3368 (2019)

## Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane.

25 September 2020 in 11:30

A. V. Lunkin, A. Yu. Kitaev, and M. V. Feigel'man

We study the SYK model with a weak quadratic perturbation, beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, fluctuations of the Schwarzian mode are suppressed, and the mean-field solution remains valid beyond the expected interval. Out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2\piT, but its prefactor scales as T at low temperatures

## Zerkal’nye pary orbifoldov Kvintiki

18 September 2020 in 11:30 (short)

B. Eremin, A. Belavin

We compare two constructions of mirror pairs of Calabi-Yau manifolds using the example of Quintic orbifolds. We consider the quotient Q/H of the original Calabi-Yau by the subgroup H of the maximal allowed group. Then the mirror variety is defined by an additional subgroup of HT as Q/HT. We compare this result with the mirror obtained in the Batyrev approach and show their equivalence.

## Localized conical edge modes and laser emission in photonic liquid crystals

11 September 2020 in 11:30 (short)

V.A. Belyakov

Most studies of the localized edge (EM) and defect (DM) modes in cholesteric liquid crystals (CLC) are related to the localized modes in a collinear geometry, i.e. for the case of light propagation along the spiral axis. Much less attention was paid to the localized modes in CLC for a non-collinear geometry. It is due to the fact that all photonic effects in CLC are most pronounced just for the collinear geometry and also partially due to the fact that a simple exact analytic solution of the Maxwell equations is known for the collinear geometry, whereas for a non-collinear geometry there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. It is why in papers related to the localized modes in CLC for a non-collinear geometry and observing phenomena similar to the case of a collinear geometry their interpretation is not so clear. Problems related to the localized modes for a non-collinear geometry are studied here in the two wave dynamic diffraction theory approximation. The dispersion equation for non-collinear localized edge modes (called conical modes (CEM)) is found and analytically solved for the case of thick layers and for this case found the lasing threshold and the conditions of the anomalously strong absorption effect. Shown that qualitatively CEMs are very similar to the EMs, however differing by their polarization properties (the CEM eigen polarizations are elliptical one depending on the degree of CEM deviation from the collinear geometry in contrast to the circular eigen polarizations in the EM case). What is concerned of the CEM quantitative values of the parameters they are “worth” than for the corresponding ones for EM. The CEM lasing threshold is higher than the one for EM and etc. Performed theoretical studies of possible conversion of EMs into CEMs showed that it can be due to the EM reflection at dielectric boundaries at the conditions of a high pumping wave focusing. Known experimental results on the CEM are discussed and optimal conditions for CEM observations are formulated.
1. V.A. Belyakov, S.V. Semenov, Localized conical edge modes of higher orders in photonic liquid crystals, Crystals, 9(10), 542 (2019);
2. V.A. Belyakov, Localized Conical Edge Modes in Optics of Spiral Media (First Diffraction Order), Crystals, 9(12), 674 (2019).

## Non-Abelian evolution systems with conservation laws and symmetries

11 September 2020 in 11:30

V.V. Sokolov

We find noncommutative analogs for well-known integrable polynomial systems of differential equations in two unknowns.
1. V. Sokolov, T. Wolf, Non-commutative generalization of integrable quadratic ODE systems, Lett. Math. Phys., 110(3), 533-553 (2020)
2. V.E. Adler, V.V. Sokolov, Non-Abelian evolution systems with conservation laws, arXiv:2008.09174

## Maxwell equations in curved space-time: non-vanishing magnetic field in pure electrostatic systems

4 September 2020 in 11:30

N.N. Nikolaev and S.N. Vergeles

Solutions of the Maxwell equations for electrostatic systems with manifestly vanishing electric currents in the curved space-time for stationary metrics are shown to exhibit a non-vanishing magnetic field of pure geometric origin. In contrast to the conventional magnetic field of the Earth it can not be screened away by a magnetic shielding. As an example of practical significance we treat electrostatic systems at rest on the rotating Earth and derive the relevant geometric magnetic field. We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings.

## Lyapunov exponent for Whitney's problem with random drive

4 September 2020 in 11:30

Nikolai A. Stepanov, Mikhail A. Skvortsov

We consider the statistical properties of a non-falling trajectory in the Whitney problem of an inverted pendulum excited by an external force. In the case when the external force is white noise, we recently found the instantaneous distribution function of the pendulum angle and velocity over an infinite time interval using a transfer-matrix analysis of the supersymmetric field theory. Here, we generalize our approach to the case of finite time intervals and multipoint correlation functions. Using the developed formalism, we calculate the Lyapunov exponent, which determines the decay rate of correlations on a non-falling trajectory.

## Inverted pendulum driven by a horizontal random force: statistics of the non-falling trajectory and supersymmetry

5 June 2020 in 11:30

Nikolay Stepanov, Mikhail Skvortsov

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction. Considered at the entire time axis, the problem admits a unique solution which always remains in the upper half plane. We develop a new technique for treating statistical properties of this unique non-falling trajectory. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistics of the non-falling trajectory is expressed in terms of the zero mode of a corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, but it is rather written for the «square root» of the distribution function.
We derive the specific boundary conditions that correspond to the non-falling trajectory. Our results for the distribution function of the angle and its velocity at the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of very strong noise, an exact analytical solution is obtained.

## Painleve equations from bilinear relations on Nekrasov partition functions

29 May 2020 in 11:30

M. Bershtein

I plan to talk about explicit formulas for solutions of the Painlevé equations and their q-difference analogues. The formulas for generic solutions are written in terms of the Nekrasov partition functions or (according to the AGT correspondence) in terms of conformal blocks. Technically, these equations are reduced to bilinear relations on the partition functions. I plan to talk about the geometric meaning of these bilinear relations.

## Coincidences between Calabi-Yau manifolds of Berglund-Hubsch type and Batyrev polytopes

22 May 2020 in 11:30

M. Belakovskij, A. Belavin

In this article, we consider the phenomenon of complete coincidence of the key properties of pairs of Calabi-Yau manifolds realized as hypersurfaces in two different weighted projective spaces. More precisely, the first manifold in such a pair is realized as a hypersurface in a weighted projective space, and the second as a hypersurface in the orbifold of another weighted projective space. The two manifolds in each pair have the same Hodge numbers and special K\"ahler geometry on the complex structure moduli space and are associated with the same $N=2$ gauge linear sigma model. We give the explanation of this interesting coincidence using the Batyrev's correspondence between Calabi-Yau manifolds and the reflexive polyhedra.

## Strange metal state near quantum superconductor-metal transition in thin films

1 May 2020 in 11:30

K.S. Tikhonov, M.V. Feigel'man

We develop a theory of quantum T=0 phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations of the Cooper attraction constant. When strength of these fluctuations exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance as inverse power of distance, with power exponent slightly larger than 2. We treat this interaction by means of strong-disorder real-space renormalization group and find the RG flow formally similar to the Berezinski-Kosterlitz-Thouless RG for 2D XY model. Line of fixed points of this RG corresponds to a Griffiths phase of a metal with large fractal clusters of strongly coupled superconducting islands. Superconducting side of the transition is characterized by a non-monotonic variation of physical properties with logarithm of the temperature T, which results of a very weak T-dependence in a broad temperature range.

## Disorder-induced rippled phases and multicriticality in free-standing graphene

24 April 2020 in 11:30

I.S. Burmistrov

One of the most exciting phenomena observed in crystalline disordered membranes, including a suspended graphene, is rippling, i.e. a formation of static flexural deformations. Despite an active research, it still remains unclear whether the rippled phase exists in the thermodynamic limit, or it is destroyed by thermal fluctuations. We demonstrate that a sufficiently strong short-range disorder stabilizes ripples, whereas in the case of a weak disorder the thermal flexural fluctuations dominate in the thermodynamic limit. The phase diagram of the disordered suspended graphene contains two separatrices: the crumpling transition line dividing the flat and crumpled phases and the rippling transition line demarking the rippled and clean phases. At the intersection of the separatrices there is the unstable, multicritical point which splits up all four phases. Most remarkably, rippled and clean flat phases are described by a single stable fixed point which belongs to the rippling transition line.

## Integrable discrete equations on a triangular lattice and second-order evolution chains

10 April 2020 in 11:30 (short)

In the talk, I will discuss the examples of integrable differential-difference equations of order 2 with respect to the discrete variable constructed in [1]. Over the past few years, some particular classification results have been obtained for such type equations, but their general description remains a very difficult open problem. The considered examples are related with continuous symmetries of discrete equations on a triangular lattice. I demonstrate that their linear combination can be written as a scalar chain of order 2, under restriction at one of the lattice axes. Although this construction is rather special, helps to significantly expand the list of known examples. [1] V.E. Adler. Integrable seven-point discrete equations and second-order evolution chains. Theor. Math. Phys. 195:2 (2018) 513-528.

## Solitonnaya turbulentnost’ na poverkhnosti glubokoi vody

10 April 2020 in 11:30 (short)

A.I. Dyachenko, S.V. Dremov, D.I. Kachulin

It is studied long-time dynamics of solitons in the frame of the super compact Zakharov equation for unidirectional waves. It is shown that after multiple collisions of breathers (solitons), only one soliton having initially a larger number of particles survives. Besides, it was found numerically bi-solutions solutions in the framework of both super compact and fully nonlinear equations.

## Extreme in amplitude bursts of signal intensity in optical communication lines

27 March 2020 in 11:30 (short)

S.S. Vergeles, S. Derevyanko, A. Redyuk, S. Turitsyn (on-line)

We investigate the bursts of intensity in a telecommunication communication line that arise as a result of the action of chromatic dispersion during the propagation of a signal with quasi-random information encoded in it. As encodings, we consider the model format of sequential pulses of a Gaussian shape and the OFDM (orthogonal frequency division multiplexing) format used in practice. The communication line is assumed to be long, so that the pulses corresponding to the bits of information become broadened due to the dispersion so much that a large number of such pulses are overlapped at one point. The initial phase pulse multipliers can take a fixed set of values, constituting the encoding alphabet. Bursts of intensity are the result of the fact that the incident phases of the pulses, acquired as they propagate along the transmission line, may (partially) compensate for the phases of the symbols of the alphabet. As a result, constructive interference of the pulse fields occurs. Such events can be attributed as random. With a fixed distance travelled by the signal, there is a maximum possible value for the amplitude of such bursts. We investigate bursts of amplitude close to the limiting for the two indicated formats: we establish their amplitude and profile. Further, we carry out numerical modelling and take into account the influence of weak nonlinearity. Finally, we examine how the capacity of the communication channel decreases if it uses primarily sequences of characters that result in strong bursts of amplitude at a fixed distance from the beginning of the line.

## O vliyanii konechnosti shaga pri sluchainom bluzhdanii na ploskosti na tochnost’ otsenki veroyatnosti pervogo peresecheniya

13 March 2020 in 11:30 (short)

L.N. Shchur

Поставлен вопрос о влиянии конечности шага на оценку вероятности пересечения окружности при случайном блуждании на плоскости. Численно выявлена зависимость точности оценки от величины шага. Предложен аналитический вид зависимости. Предложен эффективный алгоритм изменения величины шага.
[1] Olga Klimenkova, Anton Menshutin, Lev N. Shchur, "Influence of the random walk finite step on the first-passage probability", Physics and beyond (CSP2017), 9-12 Oct., 2017, Moscow
[2] Olga Klimenkova, Anton Yu. Menshutin, Lev N. Shchur, "Variable-step-length algorithms for a random walk: hitting probability and computation performance", Computer Phys. Commun., 241, 28-32 (2019)

## Spin-torque resonance due to diffusive dynamics at a surface of a topological insulator

6 March 2020 in 11:30

Pavel Ostrovsky

We investigate spin-orbit torques on magnetization in an insulating ferromagnetic layer that is brought into close proximity to a topological insulator (TI). In addition to the well-known fieldlike spin-orbit torque, we identify an anisotropic anti-damping-like spin-orbit torque that originates in a diffusive motion of conduction electrons. This diffusive torque is vanishing in the limit of zero momentum (i.e., for a spatially homogeneous electric field or current), but it may, nevertheless, have a strong impact on spin-torque resonance at finite frequency provided the external field is neither parallel nor perpendicular to the TI surface. The required electric-field configuration can be created by a grated top gate.

## Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO

6 March 2020 in 11:30 (short)

Pavel Ostrovsky

The presence of both inversion (P) and time-reversal (T) symmetries in solids leads to a well-known double degeneracy of the electronic bands (Kramers degeneracy). When the degeneracy is lifted, spin textures can be directly observed in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is very difficult to observe directly. Here, we use quantum interference measurements combined with first-principle band structure calculations to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type 3D Dirac material Sr3SnO. We find robust weak antilocalization (WAL) independent of the position of EF. The observed WAL signal at low doping is fitted using a single interference channel, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement, giving rise to robust WAL. Our work sheds light on the subtle role of spin and pseudospin, when both could contribute to the same quantum effect.

## Lattice models, deformed Virasoro algebra and reduction equation

28 February 2020 in 11:30 (short)

M.Lashkevich, Y.Pugai, J.Shiraishi, Y.Tutiya

The deformed Virasoro algebra is closely related to the so called RSOS (restricted solid-on-solid) models, which are two-dimensional exactly solvable lattice models of statistical mechanics. An important role in studying these models belongs to form factor, i.e. matrix elements in the quantum space of the transfer matrix with respect to eigenvectors of the transfer matrix. These form factors are explicitly expressed in terms of traces of vertex operators over representations of the deformed Virasoro algebra. It was observed some time ago that some excitations in the quantum space of RSOS models coincide. Nevertheless, the explicit expressions for the corresponding matrix elements differ, and their coincidence can only be established by numerical evaluation or expansions in small parameters. We found a homotopy operator that relates representatives of coincident excitations in the free field representation of the deformed Virasoro algebra. Thus, we showed that the corresponding traces over representation of the deformed Virasoro algebra coincide, whence the identities between form factors follow.

## Unrestricted electron bunching at the helical edge

28 February 2020 in 11:30

I.S. Burmistrov

A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>½$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=½$ the Fano factor is bounded between 1 and 2, generalizing earlier studies. Based on paper P.D. Kurilovich, V.D. Kurilovich, I.S. Burmistrov, Y. Gefen, M. Goldstein "Unrestricted electron bunching at the helical edge", Phys. Rev. Lett. 123, 056803 (2019).

## Paramagnetic Meissner, vortex and 'onion' ground states in Fulde-Ferrell finite-size superconductor

14 February 2020 in 11:30

D. Vodolazov, V. Plastovetz

We theoretically find that finite size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state with Delta(r) ~ exp(-i q_{FF} r), where Delta is a superconducting order parameter) has paramagnetic Meissner, vortex and 'onion' ground states with spatially nonuniform |Delta|. These states are realized due to boundary effect when the lateral size of superconductor L ~ 1/q_{FF}. We argue, that predicted states could be observed in thin disc/square made from superconductor-ferromagnet-normal metal trilayer with L ~ 150-600 nm.

## Non-equilibrium effects in Josephson SNS junctions

14 February 2020 in 11:30

V.V. Ryazanov, T.E. Golikova (ISSP RAS)

In this talk we review recent experiments on planar submicron superconductor/normal metal/superconductor junctions which have been performed in the Laboratory of superconductivity, ISSP recently. We investigated how quasiparticles and spins injected into leads and barrier of SNS junctions affect the critical current, phase difference inversion and non-local effects.

## Coexistence of superconductivity and ferromagnetism, structure of magnetic flux in bulk single crystals of magnetic superconductors

14 February 2020 in 11:30

L.Ya. Vinnikov (ISSP RAS)

With the help of the magnetic decoration method, we investigate the structure of the magnetic flux in single-crystalline magnetic superconductors based on EuFeAs doped by phosphorus. In a single crystal of ferromagnetic superconductor EuFe2(As0:79P0:21)2 with superconducting transition temperature (Tsc=22K) by decoration technique we observe vortex structure in domains of spontaneous magnetic flux (vortex domains) near the temperature of ferromagnetic transition (TСurie= Tc =18K). In a narrow temperature interval (~1K) around Tc =18K we also observe Meissner domains, detected previously by the magnetic-force microscopy method. When temperature is lowered, we observe a domain structure (vortex domains) with changing direction of the magnetic flux.

## Inhomogeneous states in disordered superconductors

14 February 2020 in 11:30

M.A. Skvortsov

An increase in disorder in a superconductor leads to the smearing of the coherence peak and appearance of localized quasiparticle states under the average gap. At a phenomenological level, the smeared density of states was calculated by Larkin and Ovchinnikov in 1971. I will overview further developments in this filed, both from a theoretical and experimental point of view.

## Laser ablation of a multilayer target with layers of nanometer thickness

7 February 2020 in 11:30 (short)

V.A. Khokhlov, S.A. Ashitkov, N.A. Inogamov, P.S. Komarov, A.N. Parshikov, Yu.V. Petrov, S.A. Romashevskii, E.V. Struleva, V.V. Zhakhovsky

Multilayer products made of ultra-thin layers are widely used in modern science and technology. Laser exposure is used as one of the promising methods of processing such products. In this regard, we study the ablation of a layered target. A physical model is constructed, numerical simulations are performed, and experiments are carried out. The experiences are unique. Firstly, the reflection coefficient is measured. Secondly, the experiments were conducted in parallel with two different lasers with different diameters of the focusing spot. The results of calculations and experiments are consistent with an accuracy of about 10%. This allowed us to refine the model of two-temperature states and determine the strength of nickel. It is explained why, with an increase in the absorbed fluence, first the upper layer breaks in the multilayer.

## Surface density of states in superconductors with inhomogeneous pairing constant

31 January 2020 in 11:30

Ya.V. Fominov, A.A. Mazanik, M.V. Razumovskiy

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a vertical'' peculiarity of the DOS around an energy equal to the bulk order parameter $\Delta_0$, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E < \Delta_0$ and $E > \Delta_0$, so the peculiarity is asymmetric. The talk is based on the paper [Ya.V. Fominov, A.A. Mazanik, M.V. Razumovskiy, Phys. Rev. B 100, 224513 (2019)].

## Ferroelectric as topological material: Hopf fibrations, multilevel logic, negative capacitance and THz vibrations

31 January 2020 in 11:30

Igor Lukyanchuk

Formation of unusual textures of polarization is imminent for nano-scale ferroelectric samples, films, rods, and granules, where the depolarization surface effects play the crucial role. The topologically protected stability of such textures and security of information storage is coming from polarization vorticity, provided by condition of absence of the energetically-unfavorable depolarization charge. The endurance of ferroelectric formations with respect to high-energy irradiation makes them ideal for the aerospace industry, and the periodic domain walls structures can be used as a platform for terahertz radiation generators and detection devices. Polarization domains that alternate the surface charge distribution can be formed in ferroelectric thin films as an effective mechanism to confine the depolarization field to the near-surface layer and diminish the depolarization energy. However their existence have long been considered as barely possible until the direct theoretical predictions [1-3] and experimental evidences [4-6] in thin oxide-based superlattices. Very recently we have demonstrated that the effective capacitance of ferroelectric layers with domains is negative [7]. This effect is explained by the opposite orientation of the depolarizing field with respect to the field-induced averaged polarization. This phenomenon is currently considered as the platform for realization of the dissipation-free high performance nano-circuits [8]. Moreover, in sub-THz region the resonance plasmonic effect can be induced by oscillating domain walls [9] and can be suitable for design of the ultra-small low-energy THz chips. Multi-vortex [10] and skyrmion [11] states can be formed inside ferroelectric cylindrical nano-dots and nanorods to reduce the depolarization energy. We study the stability of such states and demonstrate that the topological class of the most stable topological excitations can be driven by the geometrical and electrical parameters of the system, external field and temperature. We target the multi-domain and topological excitations in FE nanodots as a platform for IT-secured multivalued logic units, breaking ground for neuromorphic computing [12,13].

[1] A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. 84, 3177 (2000).
[2] V. A. Stephanovich, I. A. Luk'yanchuk, and M. G. Karkut, Phys. Rev. Lett., 94, 047601 (2005)
[3] I. Luk'yanchuk, L. Lahoche, and A. Sene, Phys. Rev. Lett., 102, 147601 (2009)
[4] S. K. Streiffer, J. A. Eastman, D. D. Fong et al., Phys. Rev. Lett. 89, 067601 (2002);
[5] S. O. Hruszkewycz, M. J. Highland, et al., Phys. Rev. Lett.110, 177601 (2013).
[6] Yadav, A. K., Nelson,et al.. Nature, 530 (7589), 198. (2016)
[7] P. Zubko, M. Hadjimichael, S. Fernandez-Pena, A. Sené, I. Luk’yanchuk, J.-M. Triscone & J. Íñiguez, Nature, 534, 524 (2016)
[8] Khan, A. I., Chatterjee, K., Wang B. et al. Nature Materials 14, 182–186 (2015).
[9] I. Luk'yanchuk, A.Pakhomov, A.Sené, A. Sidorkin, V. Vinokur, arXiv:1410.3124
[10] G. Pascoli L. Lahoche, I. Luk'yanchuk, Integrated Ferroelectrics, 99, 60 (2008)
[11] L Baudry, A Sené, IA Luk'yanchuk, L Lahoche, and JF Scott, Phys. Rev. B 90, 024102 (2014)
[12] P.-W. Martelli, S. M. Mefire, I. Luk'yanchuk, Europhys. Lett. 111, 50001 (2015)
[13] Baudry, L., Lukyanchuk, I. & Vinokur, V. M. Sci. Rep. 7: 42196 (2017)

## Quantum phase slips in inhomogeneous Josephson junction chains

24 January 2020 in 11:30

We study coherent quantum phase-slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Schön modes). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total QPS amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.

## Dual description of $\eta$-deformed OSP sigma-models

17 January 2020 in 11:30

Alexey Litvinov

My talk will be based on joint work with M. Alfimov, B. Fegin and B. Hoare. We propose a system of fermionic screening fields depending on a continuous parameter $b$, which defines $\eta$-deformed $OSP(n|2m)$ sigma-model in the limit $b\rightarrow\infty$ and a super-renormalizable QFT in $b\rightarrow0$. In the sigma-model regime we show that leading UV asymptotic of the RG group flow equations coincides with perturbation around Gaussian theory. In perturbative regime $b\rightarrow0$ we show that the tree level two-particle scattering matrix matches the expansion of the trigonometric $OSP(n|2m)$ $R$-matrix.

## Disorder and interaction in chiral chains: Majoranas versus complex fermions.

27 December 2019 in 11:30

Mirlin A.D.

We study the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) fermions. While in the noninteracting limit both models are equivalent (in particular, belong to the same symmetry class BDI and flow towards the same infinite-randomness critical fixed point), their behavior differs drastically once interaction is added. Our density-matrix renormalization group calculations show that the complex-fermion chain remains at the noninteracting fixed point. On the other hand, the Majorana fermion chain experiences a spontaneous symmetry breaking and localizes for repulsive interaction. To explain the instability of the critical Majorana chain with respect to a combined effect of interaction and disorder, we consider interaction as perturbation to the infinite-randomness fixed point and explore correlations of wave functions that enter interaction matrix elements. Our numerical and analytical results exhibit a rich structure of critical eigenstate correlations. This allows us to identify a relevant interaction operator that drives the Majorana chain away from the infinite-randomness fixed point. For the case of complex fermions, the interaction is irrelevant.

## Effect of small dissipation on the NLS anomalous waves recurrence.

13 December 2019 in 11:30

P.G. Grinevich, P.M. Santini

We provide analytic formulas decribing the effect of small loss/gain on the recurrence of anomalous waves in the focusing Nonlinear Schrodinger equation. We show that very small loss or gain essentially affects the statistics and the character of the recurrence. In particular, our formulas explains the results of numerical simulations from the paper by O. Kimmoun, H.C. Hsu, H. Branger, M.S. Li, Y.Y. Chen, C. Kharif, M. Onorato, E.J.R. Kelleher, B. Kibler, N. Akhmediev, A. Chabchoub (2016).

## KP-2 solutions in the form of soliton sequences.

13 December 2019 in 11:30 (short)

P.G. Grinevich, S. Abenda

Some photos of the ocean surface demonstrate waves looking like lattices formed by solitons. They can be modelled by finite-gap Kadomtsev-Petviashvili 2 solutions corresponding to almost dgenerate spectral curves. We show how to construct such solutions in the first non-trivial case corresponding to GR(4,2).

## Efficient algorith for 2D Fourier transform. Implementation and comparison.

13 December 2019 in 11:30 (short)

A.O. Korotkevich

Efficient implementation of parallel algorithm for fast Fourier transformation for arrays of large dimensions, based on 1D transformation from FFTW library and block-transposition, was developed and implemented as a library. 50% Speed-up with respect to 2D Fourier transformation in standard de facto FFTW library was demonstrated on three different architectures, including multiprocessor (SMP) machines.

## Landau theory for smectic-A–hexatic-B coexistence in smectic films

6 December 2019 in 11:30

E. S. Pikina, E. I. Kats, V. V. Lebedev

We explain theoretical peculiarities of the smectic-A–hexatic-B equilibrium phase coexistence in a finite-temperature range recently observed experimentally in free-standing smectic films [I. A. Zaluzhnyy et al., Phys. Rev. E 98, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order diminishes the phase coexistence range as the film thickness decreases, shrinking it to zero at some minimal film thickness Lc, of the order of a few hexatic correlation length. We established universal laws for the temperature width of the phase coexistence range in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

## GLSM for Berglund-H ubsch type Calabi-Yau manifolds

6 December 2019 in 11:30 (short)

Alexander Belavin (with Konstantin Aleshkin)

In this note we brifely present the results of our computation of special K ahler geometry for polynomial deformations of Berglund-H ubsch type Calabi-Yau manifolds. We also build mirror symmetric Gauge Linear Sigma Model and check that its partition function computed by Supersymmetric localization coincides with exponent of the K ahler potential of the special metric.

## Quantum toroidal algebras

6 December 2019 in 11:30 (short)

Bershtein M.

Quantum toroidal algebras have been actively studied over the last 20 years. The word toroidal means that the elements of the algebra depend on two variables x, y, the pair (x, y) can be considered as a point on a two-dimensional torus. The word quantum means that these algebras are analogues of quantum groups rather than just Lie algebras. I will briefly talk about origin of these algebras (AGT correspondence, integrable systems) and then formulate some recent results relating toroidal algebras corresponding to SU(N) with different N.

## Color randomization of fast two-parton states in quark-gluon plasma in heavy ion collisions

29 November 2019 in 11:30

B.G. Zakharov

We study the color randomization of two-parton states produced after splitting of a primary fast parton in the quark-gluon plasma. We find that the color randomization of the two-parton states in the quark-gluon plasma produced in heavy ion collisions at RHIC and LHC energies is rather slow. At jet energies E= 100 and 500 GeV, for typical jet path length in the plasma in central Pb+Pb collisions, the SU(3)-multiplet averaged color Casimir of the two-parton states differs considerably from its value for the fully color randomized state. We evaluate the energy dependence for generation of the nearly collinear gluon-gluon pairs in the decuplet color state and quark-gluon pairs in the anti-sextet color states, that can lead to an anomalous baryon jet fragmentation, which are forbidden in vacuum for nucleon-nucleon collisions. Our results show that the baryon production via the color anomalous two-parton states can be important in the enhancement of the baryon/meson ratio observed in heavy ion collisions at RHIC and LHC.

## Radiative parton energy loss and baryon stopping in heavy ion collisions

29 November 2019 in 11:30 (short)

B.G. Zakharov

We study the radiative energy loss contribution to proton stopping in heavy ion collisions. The radiative parton energy loss is calculated within the light-cone path integral approach to induced gluon emission. We have found that the radiative correction can fill in partly the midrapidity dip in the net proton rapidity distribution in AA collisions at center of mass energy \sqrt{s} about 10 GeV. This energy region is of great interest in connection with the beam energy scan program at RHIC (Brookhaven) and future experiments at collider NICA (Dubna) motivated by searching for the QCD critical point. We show that the net proton fluctuations at midrapidity, that have been proposed to be a good probe of the QCD critical point, may be dominated by the initial fluctuations of the proton flow, which, to a good accuracy, should be binomial, even in the presence of the critical point.

## Relaxation dynamics of nonequilibrium electrons in laser-excited solids

29 November 2019 in 11:30

Baerbel Rethfeld (Technische Universitaet Kaiserslautern, Germany)

When an ultrashort laser pulse of visible light is absorbed by a solid, mainly the electrons in the material are excited. In metals, free electrons in the conduction band can directly absorb photons. In semiconductors and dielectrics, on the other hand, a band gap has to be overcome first, as almost no free electrons are present at room temperature in the unexcited material. Due to this excitation, the electronic system, or the so-called electron-hole plasma, is in a nonequilibrium state. A sequence of different relaxation processes transfers the material into a new equilibrium. Depending on the interaction associated with the particular relaxation process, it occurs on a characteristic timescale. On the basis of complete Boltzmann-type collision integrals, we calculate the transient distribution functions of electrons and phonons in different materials. We consider electron-electron interaction, different ionization processes, as well as electron-phonon coupling. By that we trace the relaxation cascade of nonequilibrium electrons after ultrafast heating. Distinct material properties enter through the density of states of the electrons in the conduction band. We study in particular noble metals, dielectrics and ferromagnets. In noble metals and ferromagnets, d-electrons play an important role, whereas in dielectrics two separated bands govern the dynamics and the ionization state may differ from. We show, that the electron distributions deviate from Fermi distributions for timescales up to a few picoseconds. While the initial thermalization within one band has an intrinsic timescale of typically only a few tens of femtoseconds, nonequilibrium occupations of the different bands as well as continous electron-phonon coupling can drive the conduction electrons out of equilibrium for much longer times [1, 2]. We present in detail the mutual influence of different interaction and relaxation processes.
[1] N. Brouwer and B. Rethfeld, Phys. Rev. B 95, 245139 (2017). [2] S.T. Weber and B. Rethfeld, Phys. Rev. B 99, 174314 (2019).

## Hamiltonian geometry of the associativity equations

22 November 2019 in 11:30 (short)

The talk concerns the associativity equations (the WDVV system of equations), which arose in the 1990s in the papers of Witten, Dijkgraaf, and brothers Verlinde devoted to two-dimensional topological field theories. The complete classification of the associativity equations in the case of 3 primary fields with respect to the existence of a first-order Dubrovin–Novikov Hamiltonian operator will be present at the talk. Also, we consider constructed by us finite-dimensional canonical Hamiltonian reductions of the associativity equations in the cases of 3 and 4 primary fields. The talk is based on joint work with O.I. Mokhov.

## Geometry of level lines of quasiperiodic functions and related problems

15 November 2019 in 11:30

A.Ya. Maltsev

The report will provide an overview of the results so far obtained in the problem of describing the geometry of level lines of quasiperiodic functions on a plane and problems associated with it. In particular, we will consider cases of quasiperiodic functions on a plane with different numbers of quasiperiods, as well as features of the behavior of trajectories of dynamical systems associated with such functions (and also some of their generalizations). As can be shown, in many interesting cases, the trajectories of such systems can be represented by a finite number of different types corresponding to various nontrivial sets in the parameter space of such systems. As an example of dividing the parameter space into such sets, one can address to the division of the angular diagrams of the conductivity of metals in strong magnetic fields into a finite number of complexity classes.

## Master-symmetry of the KdV equation and step-like solutions

15 November 2019 in 11:30

We study solutions of the KdV equation governed by the stationary equation for symmetries from a non-commutative subalgebra, namely, for a linear combination of the master-symmetry, the dilation symmetry and the Galilean boost. The constraint under study is equivalent to a non-autonomous ODE of order 6 possessing two first integrals. Its generic solutions have a singularity on the line $t=0$. The regularity condition distinguishes a 3-parameter family of solutions, for $t=0$ satisfying an equation equivalent to $P_5$. This family describes oscillations with a power-law decrease. Numerical experiments show that in this family it is possible to distinguish a 2-parameter subfamily of separatrix solutions which tend to different constants for $x\to\pm\infty$. Qualitatively, such step-like solutions resemble the Gurevich--Pitaevsky solution for the problem of decay of the initial discontinuity, but they are not rapidly decreasing.

## Zeeman spin-orbit coupling and magnetic quantum oscillations in antiferromagnetic conductors

8 November 2019 in 11:30

P.D. Grigoriev, R. Ramazashvili, M. V. Kartsovnik

Using the symmetry arguments we show that in many metals with antiferromagnetic ordering the effective g-factor of charge carries, measured from magnetic quantum oscillations, is exactly zero. The experimental study of this effect is performed in several compounds and compared with the proposed theory. We find that the Néel state of the layered organic conductor κ-(BETS)2FeBr4 shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to the paramagnetic state of the same material. This is evidence of spin degeneracy of Landau levels -- a direct manifestation of the generic Zeeman spin-orbit coupling, predicted for antiferromagnetic conductors. Likewise, we find no spin modulation in the angle dependence of the slow Shubnikov-de Haas oscillations in the optimally electron-doped cuprate Nd2−xCexCuO4. This points to the presence of Néel order in this superconductor even at optimal doping.

## Competition of band anticrossing and charge-density wave

8 November 2019 in 11:30 (short)

P.D. Grigoriev, P.A. Vorobyev, A.A. Sinchenko

We calculate the electron susceptibility of rare-earth tritelluride compounds RTe3 as a function of temperature, wave vector, and electron-dispersion parameters. Comparison of the results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to make predictions about the evolution of electron-dispersion parameters with the variation of the atomic number of rare-earth elements (R). Our measurements of the Hall coefficient in RTe3 compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We propose that this effect may result from the interplay between two instabilities: band crossing of the Te px and py orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in the Hall effect measurements.
[1] P.A. Vorobyev, P.D. Grigoriev, K.K. Kesharpu and V.V. Khovaylo, Materials 12, 2264 (2019).
[2] P.D. Grigoriev, A.A. Sinchenko, P.A. Vorobyev, A. Hadj-Azzem, P. Lejay, A. Bosak, P. Monceau, Phys. Rev. B 100, 081109(R) (2019).

## Toward defeating diffraction and randomness for laser beam propagation in turbulent atmosphere

8 November 2019 in 11:30 (short)

Pavel Lushnikov

A large distance propagation in turbulent atmosphere results in disintegration of laser beam into speckles. We find that the most intense speckle approximately preserves both the Gaussian shape and the diameter of the initial collimated beam while loosing energy during propagation. One per 1000 of atmospheric realizations produces at 7km distance an intense speckle above 28% of the initial power. Such optimal realizations create effective extended lenses focusing the intense speckle beyond the diffraction limit of vacuum propagation. Atmospheric realizations change every several milliseconds. We propose to use intense speckles to greatly increase the time-averaged power delivery to the target plane by triggering the pulsed laser operations only at times of optimal realizations. Resulting power delivery and laser irradiance at the intense speckles well exceeds both intensity of diffraction-limited beam and intensity averaged over typical realizations.

## Column coherent vortices in a rapidly rotating turbulent fluid: a minimal theory

1 November 2019 in 11:30

S.S. Vergeles, L.L. Ogorodnikov, I.V. Kolokolov

We investigate analytically, what is a mechanism surviving a column coherent vortex is statistically steady state in rapidly rotating turbulent three-dimensional incompressible fluid. The Rossby number is assumed to be small both for small-scale eddies and the large-scale coherent vortex, which axis is directed along the rotation axis. The small-scale eddies are assumed to be excited by a random force with homogeneous statistics in time and space. The fast dynamics of the eddies is dynamics of inertia waves. Within rapid distortion theory approach, we track how the inertia waves are affected by local shear flow produced by the differential rotation in the vortex before they die out due to viscosity. We show that the shear flow influence leads to the power of the excitation force is transferred via the small eddies to the vortex, where it is dissipated due to viscosity. We establish equation determining the radial mean velocity profile in the vortex and find the profile itself.

## Zeroes of S-matrix entries and random 'anti-lasing'

25 October 2019 in 15:00

Yan V. Fyodorov (Dept. of Mathematics, King’s College London)

Motivated by recent experimental interest in 'random anti-lasing' (e.g. K. Pichler et al. Nature 567, 351 (2019)) I consider manifestations of zeroes of scattering matrices in wave-chaotic cavities. In particular, I will introduce the notion of Reflection Time Difference playing the same role for the S-matrix zeroes as the Wigner time delay plays for the S-matrix poles, and a possibility of its experimental measurement. I will then discuss how statistics of complex zeroes of scattering matrix entries can be described in the framework of RMT-based model of resonance scattering.
Presentation will be based on papers arXiv:1908.06920 and J. Phys. A 50, 30LT01 (2017).

## GENERALIZED KA¨HLER GEOMETRY IN KAZAMA-SUZUKI COSET MODELS

11 October 2019 in 11:30

S.E. Parkhomenko

It is shown that Kazama-Suzuki conditions for the denominator subgroup of N=2 superconformal G/H coset model determine Generalized K¨ahler geometry on the target space of the corresponding N=2 supersymmetric σ-model.

## Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane

4 October 2019 in 11:30

I.S. Burmistrov

We compute the absolute Poisson's ratio $\nu$ and the bending rigidity exponent $\eta$ of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality $d = 2 + d_c$, $d_c \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the absolute Poisson's ratio approaches material independent value determined solely by the spatial dimensionality $d_c$: $\nu = -1 +2/d_c-a/d_c^2+\dots$ where $a\approx 1.76\pm 0.02$. Also, we find the following expression for the exponent of the bending rigidity: $\eta = 2/d_c+(73-68\zeta(3))/(27 d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.

## The effect of anomalous elasticity on the bubbles in van der Waals heterostructures

4 October 2019 in 11:30 (short)

I.S. Burmistrov

It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the non-linear plate theory as well as membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence caused by long-ranged interaction of relevant thermal fluctuations (flexural phonons), is responsible for the anomalous Hooke's law observed recently in graphene. It is shown that this anomalous elasticity affects dependence of the maximal height of the bubble on its radius and temperature. We identify the characteristic temperature above which the anomalous elasticity is important. It is suggested that for graphene-based van der Waals heterostructures the predicted anomalous regime is experimentally accessible at the room temperature.

## Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links

27 September 2019 in 11:30 (short)

V.P. Ruban

Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation witha space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many tens of typical vortex turnover periods. [PRE 100, 012205 (2019)].

## Contact Probability in Loop Extrusion Model of Interphase Chromosome

27 September 2019 in 11:30

S. Belan (in collaboration with Mirny Lab, MIT)

Due to the development of the chromosome conformation capture (Hi-C) method, it has become possible to get insight into the chromatin organization by measuring the frequency of physical contacts between different parts of genome. The mechanism of active loop extrusion holds great promise for explaining the key features of the contact maps obtained from the Hi-C data. The loop extrusion model assumes that ATP-dependent process allows nanometer-size molecular machines to organize chromosomes by producing dynamically expanding chromatin loops. In this talk I will give a brief introduction into the loop extrusion model and demonstrate that analytical predictions extracted from this model in its simplest version, where chromatin fiber is treated as an ideal Gaussian chain, are in agreement with experimentally measured statistics of contacts in the interphase chromosomes.

## High order Fano-resonances and extreme effects in field localization

20 September 2019 in 11:30

Борис Лукьянчук (МГУ & Nanyang Technological University, Singapore)

The weakly dissipating dielectric spheres (glass, quartz, etc.) permit to realize high order Fano resonances for internal Mie modes. These resonances for specific values of the size parameter yield field-intensity enhancement factors on the order of 104–107, which can be directly obtained from analytical calculations. These “super-resonances” provides magnetic nanojets with giant magnetic fields, which is attractive for many applications.

## String breaking, diquarks and medium

13 September 2019 in 11:30

Oleg Andreev

I will briefly discuss some aspects of the phenomenon of string breaking in QCD. Such a phenomenon is responsible for strong decays of hadrons. Mainly, I focus on what happens at finite baryon density.

## Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

13 September 2019 in 11:30 (short)

L. Shchur

We study the properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of the single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat.

## Parallel SPH modeling using dynamic domain decomposition and load balancing displacement of Voronoi subdomains

14 June 2019 in 11:30

Maria S. Egorova, Sergey A. Dyachkov, Anatoliy N. Parshikov, Vasily V. Zhakhovsky

A highly adaptive load balancing algorithm for parallel simulations using particle methods, such as molecular dynamics and smoothed particle hydrodynamics (SPH), is developed. Our algorithm is based on the dynamic spatial decomposition of simulated material samples between Voronoi subdomains, where each subdomain with all its particles is handled by a single computational process which is typically run on a single CPU core of a multiprocessor computing cluster. The algorithm displaces the positions of neighbor Voronoi subdomains in accordance with the local load imbalance between the corresponding processes. It results in particle transfers from heavy-loaded processes to less-loaded ones. Iteration of the algorithm puts into alignment the processor loads. Convergence to a well-balanced decomposition from imbalanced one is improved by the usage of multi-body terms in the balancing displacements. The high adaptability of the balancing algorithm to simulation conditions is illustrated by SPH modeling of the dynamic behavior of materials under extreme conditions, which are characterized by large pressure and velocity gradients, as a result of which the spatial distribution of particles varies greatly in time. The higher parallel efficiency of our algorithm in such conditions is demonstrated by comparison with the corresponding static decomposition of the computational domain. Our algorithm shows almost perfect strong scalability in tests using from tens to several thousand processes.
Publications: arXiv:1805.05128v2 [physics.comp-ph] ; Computer Physics Communications, Volume 234, January 2019, Pages 112-125

## Termal’nyi effekt Kholla kak topologicheskii invaraint

7 June 2019 in 11:30

Lev Spodyneiko

We show that derivatives of thermal Hall conductance of a 2d lattice quantum system with respect to parameters of the Hamiltonian are well-defined bulk quantities provided correlators of local observables are short-range. This is despite the fact that thermal Hall conductance itself has no meaning as a bulk transport coefficient. We use this to define a relative topological invariant for gapped 2d lattice quantum systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes bulk-boundary correspondence for the chiral central charge. We also show that for Local Commuting Projector Hamiltonians relative thermal Hall conductance vanishes identically, while for free fermionic systems it is related to the electric Hall conductance via the Wiedemann-Franz law.

## Dissipative and Hall viscosity of a disordered 2D electron gas

7 June 2019 in 11:30

I.S. Burmistrov

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity. Here we address this question, both analytically and numerically, in the context of a disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of weak (strong) magnetic field and strong (weak) disorder. In the regime of weak magnetic field our results describes the quantum (Shubnikov-de Haas type) oscillations of the dissipative and Hall viscosity. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the viscosity coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity is surprisingly robust to disorder.

## Formation and decay of eddy currents generated by crossed surface waves

31 May 2019 in 11:30

Parfenyev V.M., Filatov S.V., Brazhnikov M.Yu., Vergeles S.S., Levchenko A.A.

The mass-transport induced by crossed surface waves consists of the Stokes and Euler contributions which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and it is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass-transport theoretically and experimentally and demonstrate that both contributions have different time scales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution evolves faster, feeling the additional damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film presented on the fluid surface with the compression modulus being the only non-zero rheological parameter of the film. Then the Euler contribution into the mass-transport becomes parametrically larger and the evolution of the Stokes contribution becomes parametrically faster. The parameter is the same in both cases and it is equal to the quality factor of surfaces waves, which is modified by the presence of a surface film. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

## Bernoulli Experiment under Restart

31 May 2019 in 11:30

S. Belan

It is known that restart of the stochastic process can significantly reduce the expected time required to its completion. This effect is widely implemented to speed up the randomized search algorithms and can potentially be used to increase the rate of chemical reactions. However, complex stochastic processes often exhibit several possible scenarios of completion which are not equally desirable in terms of efficiency. In this talk I will discuss how restart affects the splitting probabilities of a Bernoulli-like stochastic process, i.e., of a process which can end with one of two outcomes. Special attention will be paid to the class of problems, where a carefully tuned restart rate maximizes the chances to obtain the desired outcome. Importantly, the analysis revealed universality displayed by the optimally restarted processes.

## Aspects of quarkonium propagation in a thermal medium as seen by string models

17 May 2019 in 11:30 (short)

Oleg Andreev

We use gauge/string duality to model a heavy quark-antiquark pair in a color singlet moving through a thermal plasma. In particular, we explore the effect of velocity on the string tension and Debye screening mass. Then we apply the results to the analysis of heavy quarkonium bound states. With some assumptions, we estimate the characteristic size of quarkonium and its dissociation temperature.

## Some exact solutions of the Volterra lattice

19 April 2019 in 11:30

We study solutions of the Volterra lattice satisfying the stationary equation for its non-autonomous symmetry. It is shown that the dynamics in $t$ and $n$ are governed by the continuous and discrete Painlev\'e equations, respectively. The class of initial data leading to regular solutions is described. For the lattice on the half-line, these solutions are expressed in terms of the confluent hypergeometric function. The Hankel transform of the coefficients of the corresponding Taylor series is computed on the basis of the Wronskian representation of the solution.

## CDD factors in integrable models perturbed by the current-current operators

29 March 2019 in 11:30

M. Lashkevich, Y. Pugai

F. Smirnov and A. Zamolodchikov in the paper published in 2016 showed that a special class of irrelevant perturbations (current-current perturbations) in integrable models of quantum field theory leads to appearance of CDD factors in the scattering matrices, i.e. scalar factors corresponding to non-uniqueness of solution to the Yang-Baxter equation for S matrices. They considered the sine-Gordon model and analogous models that only contain odd-spin integrals of motion. We find CDD factors (in the first order in the perturbation theory) for the current-current perturbations on the example of models that contain even-spin integrals of motion as well, the complex sinh-Gordon model and the scaling Z_N symmetric Ising model. Thus we generalize the Smirnov-Zamolodchikov formula to the case of several particles with diagonal scattering. We also obtain the CDD factors for Lorentz non-invariant perturbations of this type. Technically we use the representation by free fields for form factors, developed by us earlier.

## Studies of the Liquid Crystal Surface Anchoring Potential using Grandjean-Cano Wedge

22 March 2019 in 11:30 (short)

V.A. Belyakov

We extend further the theoretical and experimental studies of the actual surface anchoring potential restoration by polarization microscope technique and using micro-images in a wedge-shaped cell with weak surface anchoring forces filled by a chiral nematic liquid crystal (in Grandjean-Cano Wedge). To realize the theoretically predicted options of observation of large director deviation angles from the easy axes the experimental studies of director distribution in Grandjean-Cano zones were performed for differing easy axes orientations at the wedge surfaces in white light. A weak surface anchoring at one wedge surface was obtained by a photo-alignment technique. A strong surface anchoring at the second wedge surface was obtained by a rubbing. There were observed for the first time jump-less walls (without jumps of the director orientation) between neighboring Grandjean-Cano zones and jumps in color in the Newton's rings (lines) at the positions of the walls between Grandjean-Cano zones. Qualitative explanations of the both phenomena are presented and an expression for the jump in color value in the Newton's rings (lines) at the positions of the walls between Grandjean-Cano zones is presented. Some experimentally found by the polarization microscope and by the micro-photo technique images demonstrate jump-less walls between the first Grandjean-Cano zones. To ensure optimal parameters of the further experiments on the actual surface anchoring potential restoration theoretical calculations of the director distribution in individual Grandjean-Cano zones were performed for various model surface anchoring potentials. It was found that especially promising for description of the experimentally found director distribution looks the modified D-potential. As a result of the present studies the ways to enlarge (compared to the previous studies) angular range of the actual surface anchoring potential restoration were proposed.
(The presentation is based at the following papers: V.A. Belyakov, D.V. Shmeliova, S.V. Semenov, On the way of reconstruction of the liquid crystal surface anchoring potential Journal of Molecular Liquids 267, 151–157 (2018), С. В. Семенов, В. А. Беляков, ПОВЕРХНОСТНОЕ СЦЕПЛЕНИЕ И РАСПРЕДЕЛЕНИЕ ДИРЕКТОРА В КЛИНЕ ГРАНЖАНА–КАНО, ЖЭТФ, 2018, том 153, вып. 5, стр. 838–844 ( 2018), V.A.Belyakov , D.V.Shmeliova, and S.V. Semenov, Studies of the Liquid Crystal Surface Anchoring Potential using Grandjean-Cano Wedge, LIQUID CRYSTALS (Published online: https://doi.org/10.1080/02678292.2018.1546412).

## Boundary layer of elastic turbulence

15 March 2019 in 11:30 (short)

S. Belan, A. Chernykh, V. Lebedev

We consider the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. We examine analytically and numerically statistics of the polymer conformation in the boundary layer. An estimate for the ratio of the mean flow to the magnitude of flow fluctuations is obtained. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

## Physical processes during laser ablation into a liquid and during laser shock-wave pinning

15 March 2019 in 11:30 (short)

V.A. Khokhlov, N.A. Inogamov, V.V. Zhakhovsky,Yu.V. Petrov, S.I.Anisomov

The most important modern laser technologies include (1) the generation of colloid nanoparticles (NPs), laser ablation into a liquid (LAL—laser ablation in liquid) and (2) surface hardening of products by laser pinning (LSP—laser shock peening). Significantly, with laser pinning, the surface to be treated is washed with water. Therefore, the physics of processes during ablation into a liquid and during pinning is common. True, the accents are different. If the ablation in the liquid actually forget about the shock wave (SW) generated by the impact, and leaving the thickness of the target, in the problem with pinning, on the contrary, the main question is about the impact. In addition, the role of water in (1) and (2) is different. In (1) fluid contributes to the formation of NPs and adopts NPs, gently slowing them. Whereas in (2) water is needed to enhance the recoil and increase the amplitude of the hydrocarbon in the product. The complete picture, developed in the work, of course, should include both edges: and the formation of ejection into the liquid as a result of ablation—i.e. (1), observation of the SW wave from the nucleation stage to its attenuation in the product volume, i.e. (2).

## Laser technologies: science and applications

15 February 2019 in 11:30

N.A. Inogamov

In the first part of report the combined action of laser and plasmonic electromagnetic fields which dissipate in a metal film is considered. Fast dissipation of energy of light causes mechanical response moving a film. Motion and subsequent fast re-crystallization result in formation of surface micro-structures used for holographic purposes [1,2]. In the second part the physics of laser fragmentation of a liquid tin micro-droplet is analyzed. This is important for development of next generation of photo-lithography machines [3]. In the third part the indirect monitoring shot-to-shot shock waves strength reproducibility during the pump-probe experiments is studied [4]. The calibrated laser source is used after this checking for generation of shocks; goals for employing of these shocks are described in Albertazzi et al., Science Advances, 3(6), e1602705 (2017). [1] J. Phys.: Conf. Ser., 1092, 012051 (2018) [2] J. Phys.: Conf. Ser., 1092, 012052 (2018) [3] Phys. Rev. Applied 10, 064009 (2018) [4] J. Appl. Phys. 120, 035901 (2016)

## Shock generation by laser and impact initiation of burning

15 February 2019 in 11:30

N.A. Inogamov

Generation of shocks by an ultrashort laser pulse is considered. Elastic-plastic response and polymorphic alpha-epsilon transition in iron are analyzed [1,2]. Initiation of initial stages of burning of high explosives by slow impact is studied [3]. Burning is caused by dissipative heating during plastic deformations.
[1] S.I. Ashitkov, V.V. Zhakhovsky, N.A. Inogamov, P.S. Komarov, M.B.Agranat, and G.I.Kanel, The behavior of iron under ultrafast shock loading driven by a femtosecond laser, AIP Conf. Proc. 1793, 100035 (2017) [2] V.V. Zhakhovsky, K.P. Migdal, N.A. Inogamov, S.I. Anisimov, MD simulation of steady shock-wave fronts with phase transition in single-crystal iron, AIP Conf. Proc. 1793, 070003 (2017) [3] D. Ilnitsky, N. Inogamov, V. Zhakhovsky, Response of explosive HMX to low-velocity impact: Modeling by the crystal plasticity finite element method, J. Phys.: Conf. Ser., 941, 012052 (2018)

## Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate

8 February 2019 in 11:30 (short)

V.P. Ruban

Dynamics of simplest vortex knots, unknots, and links of torus type inside an atomic Bose-Einstein condensate in anisotropic harmonic trap at zero temperature has been numerically simulated using three-dimensional Gross-Pitaevskii equation. The lifetime for such quasi-stationary rotating vortex structures has been found quite long in wide parametric domains of the system. This result is in qualitative agreement with a previous prediction based on a simplified one-dimensional model approximately describing dynamics of vortex filaments.

## CALCULATION OF THE DISCRETE SPECTRUM OF SOME TWO-DIMENSIONAL SCHR¨ODINGER EQUATIONS WITH A MAGNETIC FIELD

8 February 2019 in 11:30

V.G. Marikhin, A.V. Marikhina

One of us previously obtained and integrated the first examples of two-dimensional Schr¨odinger equations with a magnetic field belonging to the class of quasi–exactly solvable problems. It was shown that the wave functions are expressed in terms of degenerations of the Heun function: biconfluent and confluent Heun functions. Algebraic conditions were also found that determine the discrete spectrum and wave functions. Our goal here is to solve these algebraic equations numerically. In some cases, we can find an analytic approximation of the discrete spectrum.

## Hermite quasi-polynomials

8 February 2019 in 11:30 (short)

V.G. Marikhin

The Hermite quasi-polynomials are obtained (the square root of the weight coincides with the Hermite one). The corresponding spectral problem with singularity at zero is constructed. The space to which belong the eigenfunctions of the above-mentioned spectral problem is constructed. The kind of this space solves the paradox with singularity.

## On complex angular diagrams of magnetic conductivity in strong magnetic fields

1 February 2019 in 11:30 (short)

A.Ya. Maltsev

We consider angular conductivity diagrams for normal (single-crystal) metals with complex Fermi surfaces in the presence of strong magnetic fields. The behavior of conductivity in this case strongly depends on the direction of the magnetic field and the stable nontrivial regimes of this behavior correspond to special zones of stability on the angular diagram corresponding to certain (topological) properties of the conductivity tensor. As we show, in the general case such diagrams can be divided into two general types, simple (type A) and complex (type B). We will be interested in the diagrams of the second type, which have a number of specific features (an infinite number of stability zones, the presence of chaotic regimes, etc.), which we will consider in more detail.

## Collinear photon emission from the quark-gluon plasma in heavy ion collisions

25 January 2019 in 11:30

B.G. Zakharov

Making use the light-cone path integral scheme we develop a formalism for collinear photon emission from the quark-gluon plasma (QGP) that accounts for accurately the Landau-Pomeranchuk-Migdal effect. In the case of the QGP without magnetic field we reproduce the AMY (Arnold, Moore, Yaffe (2001)) photon spectrum obtained within the thermal field theory. In the first part of the talk we study the role of running coupling and the effect of variation of the thermal quark mass on contribution of the collinear bremsstrahlung and quark-antiquark annihilation to photon emission in AA collisions in a scheme similar to that used in our previous jet quenching analyses. We find that for a scenario with the thermal quark mass about 50-100 MeV contribution of the higher order collinear processes summed with the 2 \to 2 processes can explain a considerable part (about 50%) of the experimental photon spectrum at k_T about 2-3 GeV for Au+Au collisions at $\sqrt{s}=0.2$ TeV. But for quark mass 300 MeV and for the thermal quark mass predicted by the hard thermal loop scheme the theoretical predictions underestimate considerably the experimental spectrum. In the second part of the talk we discuss a generalization of our formalism to the QGP with magnetic field. We then use it to investigate the effect of magnetic field on the photon emission from the QGP created in AA collisions. We find that even for very optimistic assumption on the magnitude of the magnetic field generated in AA collisions its effect on the photon emission rate is practically negligible. For this reason the magnetic field cannot generate a significant azimuthal asymmetry in the photon spectrum as it was suggested in the analysis by Tuchin (K. Tuchin, Phys. Rev. C{\bf 91}, 014902 (2015)).

## Recent applications of the light-cone path integral formalism to the radiative effects in $AA$-collisions due to the induced gluon/photon emission in the QCD matter

18 January 2019 in 11:30

B.G. Zakharov

In this talk I discuss some recent applications of the light-cone path integral (LCPI) approach to the induced gluon/photon emission in the quark-gluon plasma (QGP) in $AA$-collisions at RHIC-LHC energies. I start with a brief discussion of the basic formulas of the LCPI formalism. Then I present the results for the nuclear modification of the photon-tagged jets in $AA$ collisions within the jet quenching scheme based on the LCPI approach to the induced gluon emission. The calculations are performed for running coupling. Collisional energy loss is treated as a perturbation to the radiative mechanism. We obtain a reasonable agreement with the recent data from the STAR Collaboration on the mid-rapidity nuclear modification factor $I_{AA}$ for Au+Au collisions at $\sqrt{s}=200$ GeV for parametrization of running $\alpha_s$ consistent with that necessary for description of the data on suppression of the high-$p_T$ spectra. The main part of the talk will be devoted to the radiative contribution to the jet $p_T$-broadening in the QGP. For the first time the analysis of the radiative $p_T$-broadening of a fast quark in the QGP is performed accounting for the real and virtual two-parton states beyond the soft gluon approximation. It is shown that radiative processes can strongly suppress the radiative $p_T$-broadening in the QCD matter (and even make it negative). This prediction is qualitatively different from the results of previous analyses in th soft gluon approximation in the double logarithmic approximation (B. Wu, JHEP 1110, 029 (2011); T. Liou, A. H. Mueller and B. Wu, Nucl. Phys. A916, 102 (2013); J.-P. Blaizot and Y. Mehtar-Tani, Nucl. Phys. A929, 202 (2014)) predicting that radiative processes should significantly increase $p_T$-broadening. Our prediction is consistent with the recent data of the STAR Collaboration (L. Adamczyk et al., Phys.Rev. C96, 024905 (2017)), which do not show any signal of $p_T$-broadening in Au+Au collisions at the energy 200 GeV. At the end of the talk I discuss the the role of running coupling and the effect of variation of the thermal quark mass on contribution of the collinear bremsstrahlung and annihilation to photon emission in $AA$ collisions in a scheme similar to that used in our previous jet quenching analyses.

## Inelastic neutron scattering as a confirmation of a new type of gapped surface excitations in liquid helium

18 January 2019 in 11:30 (short)

P.D. Grigoriev, A.D. Grigoriev, A.M. Dyugaev

We analyze the experimental data on inelastic neutron scattering by a thin ~5-atomic-layer film of liquid helium at three different temperatures: T=0.4K, 0.98K and 1.3K. The neutron scattering intensity plots, in addition to the previously know dispersion of phonons and ripplons, suggest a branch of gapped surface excitations with activation energy ~4.5K and the dispersion similar to that expected for surfons -- the bound quantum states of helium atoms above liquid helium surface, proposed and investigated theoretically. These data, probably, provide the first direct experimental confirmation of surfons. Before these surface excitations received only indirect experimental substantiation, based on the temperature dependence of surface tension coefficient and on their interaction with surface electrons. The existence of surfons as an additional type of surface excitations, although being debated yet, is very important for various physical properties of He surface. We also analyze previous numerical results on excitations in liquid helium and argue that surface excitations similar to surfons have been previously obtained by numerical calculations and called resonance interface states.

## Linear magnetoresistance in the charge density wave state of quasi-two-dimensional rare-earth tritellurides

18 January 2019 in 11:30 (short)

P.D. Grigoriev

The magnetoresistance of a TbTe3 two-dimensional conductor with a charge-density wave (CDW) has been measured in a wide temperature range and in magnetic fields of up to 17 T. At temperatures well below the Peierls transition temperature and in high magnetic fields, the magnetoresistance exhibits a linear dependence on the magnetic field caused by the scattering of normal charge carriers by “hot” spots of the Fermi surface. In the sliding CDW regime in low magnetic fields, a qualitative change in the magnetoresistance has been observed associated with the strong scattering of carriers by the sliding CDW.
[1] A.V. Frolov, A.P. Orlov, P.D. Grigoriev, V.N. Zverev, A.A. Sinchenko, P. Monceau, Magnetoresistance of a Two-Dimensional TbTe3 Conductor in the Sliding Charge-Density Wave Regime, JETP Lett., 107(8), 488-492 (2018)

## Dual description of integrable sigma-models

11 January 2019 in 11:30

Litvinov Alexey

In my talk I will discuss an example of the weak / strong coupling duality, i.e. equivalence seemingly distinct quantum field theories, so that the strong coupling regime of one theory describes the weak coupling regime of the other, and vice versa. In my example, these are two-dimensional sigma models and boson field theories with exponential interaction. Both theories are integrable. To explain the duality, I will construct a W-algebra commuting with a set of screening operators on one side and solve the Ricci flow equation with given ultraviolet asymptotic boundary conditions.
The report is based joint work with Fateev and Spodyneiko.

## Deautonomization of cluster integrable systems

11 January 2019 in 11:30

M. Bershtein

Cluster integrable systems have a combinatorial definition in terms of counting dimer configurations on a bipartite graph on a torus. They have a large group of discrete symmetries preserving the Hamiltonian. After deautonomization, the Hamiltonians depend on time, integrability disappears, and discrete symmetry leads to remarkable difference equations, such as the Painleve equations. These equations are solved using the partition functions of five-dimensional supersymmetric theories. The talk is based on joint work with P. Gavrilenko and A. Marshakov.

## On the initial conditions in heavy ion collisions at RHIC and LHC energies

21 December 2018 in 11:30 (short)

B.G. Zakharov

We discuss our recent results on the heavy ion collisions at RHIC and LHC energies. We discuss the initial conditions for the entropy distribution in AA-collisions within the Glauber Monte-Carlo model accounting for the effect of the meson-baryon components in the nucleon light-cone wave function. Also, we discuss fluctuations of the electromagnetic fields produced in the non-central AA-collisions in the classical and quantum picture. We show that quantum calculations based on the fluctuation-dissipation theorem give fluctuations of the electromagnetic field that are much smaller than that in the classical Monte-Carlo calculations with the Woods-Saxon nuclear density widely used in the literature.

## Quantum corrections to conductivity of disordered electrons due to inelastic scattering off magnetic impurities

21 December 2018 in 11:30

I.S. Burmistrov

We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different g factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type.
The talk is based on I. S. Burmistrov and E. V. Repin, Phys. Rev. B 98, 045414 (2018)

## Magnetism of Bi2Se3 thin films with Eu-rich flat inclusions

21 December 2018 in 11:30 (short)

I.S. Burmistrov

I report about theoretical support of experimental data on the measurement of the magnetic properties of thin films of bismuth selenide doped with europium atoms, which form flat inclusions. The magnitudes of the various mechanisms of magnetic ordering are theoretically estimated. The estimates obtained are in satisfactory agreement with the experimental data.
Report is based on the paper: L.N. Oveshnikov, Ya.I. Rodionov, K.I. Kugel, I.A. Karateev, A.L. Vasiliev, Yu.G. Selivanov, E.G. Chizhevskii, I.S. Burmistrov and B.A. Aronzon, "Magnetism of Bi2Se3 Thin Films with Eu-rich flat inclusions", J. Phys .: Condens. Matter 30, 445801 (2018)

## Volterra chain and Catalan numbers

21 December 2018 in 11:30 (short)

The model problem on the decay of a step for the Volterra chain is formulated as a Cauchy problem with initial condition equal to 0 in one node and 1 in the others. We show that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for Catalan numbers. Asymptotic formulas for the solution are obtained.

## Two-sphere partition functions and Kahler potentials on CY moduli spaces

14 December 2018 in 11:30 (short)

A. Belavin, K. Aleshkin, A. Litvinov

We study the relation between exact partition functions of gauged $N=(2,2)$ linear sigma-models on $S^{2}$ and K\"ahler potentials of CY manifolds proposed by Jockers et all. We suggest to use a mirror version of this relation. For a class of manifolds given by a Fermat hypersurfaces in weighted projective space we check the relation by explicit calculation.
Aleshkin K., Belavin A., Litvinov A., “Two-sphere partition functions and Kähler potentials on CY moduli spaces”, Письма в ЖЭТФ, 108(10), 725 (2018)

## Probing spin susceptibility of a correlated two-dimensional electron system by transport and magnetization measurements

14 December 2018 in 11:30 (short)

I.S. Burmistrov

I report theoretical support of the data on measuring the spin susceptibility at different temperatures and electron concentrations in a two-dimensional electron system based on a silicon field-effect transistor in the group of V.M. Pudalov (Lebedev Institute).
The short talk is based on the work of V. M. Pudalov, A. Yu. Kuntsevich, M.E. Gershenson, I.S. Burmistrov, and M. Reznikov, Phys. Rev. B 98, 155109 (2018).

## A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current

14 December 2018 in 11:30

I.S. Burmistrov

We consider a small itinerant ferromagnet exposed to an external magnetic field and strongly driven by a thermally induced spin current. For this model, we derive the quasi-classical equations of motion for the magnetization where the effects of a dynamical non-equilibrium distribution function are taken into account self-consistently. We obtain the Landau-Lifshitz-Gilbert equation supplemented by a spin-transfer torque term of Slonczewski form. We identify a regime of persistent precessions in which we find an enhancement of the thermoelectric current by the pumping current.
The talk is based on T. Ludwig, I.S. Burmistrov, Y. Gefen, A. Shnirman, "A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current", arxiv:1808.01192

## Mesoscopic supercurrent fluctuations in diffusive magnetic Josephson junctions

23 November 2018 in 11:30

P. A. Ioselevich, P. M. Ostrovsky, Ya. V. Fominov

We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than the magnetic pair-breaking length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase relation (CPR) along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by magnetism in the link. We find that all harmonics are present in the CPR. Each harmonic has its own sample-dependent amplitude and phase shift with no correlation between different harmonics. Depending on the type of magnetic weak link, the system can realize a \varphi_0 or \varphi junction in the fluctuational regime. Full supercurrent statistics is obtained at arbitrary relation between temperature, superconducting gap, and the Thouless energy of the weak link.

## Statistics of eigenstates near the localization transition on random regular graphs

23 November 2018 in 11:30

Konstantin Tikhonov

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes below the correlation volume and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast diffusion which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate limit of the Anderson model in spatial dimensions.

## Two-temperature statistics of free energies in (1+1) directed polymers

2 November 2018 in 11:30

Victor Dotsenko

The joint statistical properties of two free energies computed at two different temperatures in the same sample of (1+1) directed polymers is studied in terms of the replica technique. The scaling dependence of the free energies differenceon the two temperatures $T_{1}$ and $T_{2}$ is derived. In particular, it is shown that if the two temperatures $T_{1} < T_{2}$ are close to each other the typical value of the fluctuating part of the free energies difference is proportional to $(1 - T_{1}/T_{2})^{1/3}$. It is also shown that the left tail asymptotics of this free energy difference probability distribution function coincides with the corresponding tail of the Tracy-Widom distribution.
Europhysics Letters, 116, 40004 (2016); arXiv:1703.04305

## Non-Born effects in scattering of electrons in clean quasi-one-dimensional conductors

26 October 2018 in 11:30

A. S. Ioselevich, N. S. Peshcherenko

Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $\nu_F$ and the resistivity $\rho$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration $n_c\propto |\lambda|$, $\lambda\ll 1$ being the dimensionless amplitude of scattering. For $n\gg n_c$ the singularities are simply rounded at $\varepsilon\equiv E-E_N\sim \tau^{-1}$ – the Born scattering rate. For $n\ll n_c$ the non-Born effects in scattering become essential, despite $\lambda\ll 1$. The peak of the resistivity is split: for $\varepsilon>0$ there is a broad maximum at $\varepsilon\propto \lambda^2$. For $\varepsilon\lt 0$ there is a deep minimum at $|\varepsilon|\propto n^2\ll \lambda^2$. The behaviour of $\rho$ below the minimum depends on the sign of $\lambda$. In case of repulsion $\rho$ monotonically grows with $|\varepsilon|$ and saturates for $|\varepsilon| \gg \lambda^2$. In case of attraction $\rho$ has sharp maximum at $|\varepsilon| \propto \lambda^2$. The latter feature is due to resonant scattering by quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.

## Electron-phonon cooling power in Anderson insulators

26 October 2018 in 11:30

M. V. Feigel'man, V. E. Kravtsov

A theory for electron-phonon energy exchange in Anderson insulators with long localization length is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function of the local density of electron states, which is enhanced near the localization transition by multi-fractality and by the presence of Mott's resonant pairs of states. The theory we develop explains huge enhancement of the cooling power observed in insulating Indium Oxide films as compared to predictions of standard theory for disordered metals

## The free field representation for the GL(1|1) WZW model revisited

12 October 2018 in 11:30

M. Lashkevich

The Wess—Zumino—Witten theory related to the GL(1|1) supergroup possesses some interesting features. On one hand, its structure is rather simple, but, on the other hand, it is an example of a so called logarithmic theory, i.e. a conformal field theory that contains fields whose correlation functions depend on distances logarithmically. The spectrum of conformal dimensions in this theory is continuous, and logarithmic operators appear at some degenerate points, including those of zero dimension. The free field representation is an effective tool to study models of the conformal field theory, and that of the GL(1|1) theory seems to be rather simple and well-studied in previous works. Nevertheless, on my opinion, not all advantages of this representation were used. In the present work, beside a more detailed calculation of the structure constants, the fusion and braiding matrices were studied. It was shown that in the vicinity of degenerate points it is possible to chose a basis of conformal blocks, which resolves degeneration. I show how this basis is related to the logarithmic operators of the theory.

## Quantum electrodynamics of heavy ions and atoms

5 October 2018 in 11:30

Vladimir Shabaev (St. Petersburg State University)

The present status of the QED theory of heavy ions and atoms is reviewed. The theoretical predictions for the Lamb shifts, the hyperfine splittings, and the bound-electron g factors of highly charged few-electron ions are compared with available experimental data. Special attention is paid to tests of QED at strong-coupling regime and determination of fundamental constants. The current status of studying the parity nonconservation effects with heavy atoms is also reported. Recent results on the charge-transfer and pair-creation probabilities in low-energy heavy-ion collisions are presented. Prospects for tests of QED at supercritical fields are discussed.

## Irreversible Markov chains: From the TASEP to all-atom Coulomb computations

28 September 2018 in 15:00

Werner Krauth, Ecole normale supérieure, Paris (France)

The Markov chain Monte Carlo method traditionally consists in exploring large configuration spaces using a reversible random walk where moves are accepted or rejected based on an energy criterion. In this talk, I will present recent progress on irreversible Markov chains that challenge this picture. In one-dimensional particle systems, the new algorithms are related to the TASEP (totally asymmetric simple exclusion model). We can rigorously prove that they mix on much shorter time scales than the reversible Metropolis algorithms. I will then show how these algorithms sample the Boltzmann distribution (and thus explore configuration space) without computing the energy. In long-range interacting systems, where the computation of the energy is time-consuming, this provides a key advantage for the new method. For locally charge-neutral systems in three dimensions, we obtain a highly efficient algorithm, of N log N complexity in the number N of particles. I discuss the main paradox of this method: How is it possible to sample the Boltzmann distribution without computing the energy, and then review some recent successes as well as prospects and challenges for irreversible Markov chains in statistical physics.
References:
S. C. Kapfer, W. Krauth, Physical Review Letters 119, 240603 (2017)
Z. Lei, W. Krauth, arXiv:1806.06786 (2018)
M. F. Faulkner, L. Qin, A. C. Maggs, W. Krauth, arXiv:1804.05795 (2018)

## Superconductivity that breaks time-reversal symmetry and its experimental manifestations

28 September 2018 in 11:30

Victor Yakovenko (University of Maryland)

Since 2006, it has been found experimentally that superconductivity spontaneously breaks time-reversal symmetry (TRS) in certain materials, such as Sr2RuO4, UPt3, URu2Si2, and Bi/Ni bilayers. In the latter case, we argue that the superconducting order parameter has the winding number of +-2 around the Fermi surface, thus making Bi/Ni bilayers a rare example of intrinsic 2D topological superconductivity [1]. The experimental evidence for TRS breaking comes from the polar Kerr effect, which is rotation of polarization of normally incident light upon reflection from the sample. Theoretical studies indicate that this effect is possible only if a superconductor has more than one band. To clarify these conditions, we study a model of chiral TRS-breaking superconductivity on the honeycomb lattice [2]. We consider superconducting pairing on the neighboring sites belonging to different sublattices. The matrix of this superconducting pairing is non-unitary and does not commute with the normal-state Hamiltonian. We find that the latter condition is necessary for experimental manifestations of the TRS breaking. We show that such superconducting pairing generates persistent loop currents around each lattice site and opens a topological mass gap at the Dirac points with the corresponding chiral edge states, as in Haldane's model of the quantum anomalous Hall effect. We calculate the intrinsic ac Hall conductivity in the absence of an external magnetic field, which determines the polar Kerr effect, and show that it is proportional to the loop-current order parameter.
[1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538
[2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

## Three-dimensional stability of leapfrogging quantum vortex rings

21 September 2018 in 11:30 (short)

V.P. Ruban

It is shown by numerical simulations within a regularized Biot-Savart law that dynamical systems of two or three leapfrogging coaxial quantum vortex rings having a core width $\xi$ and initially placed near a torus of radii $R_0$ and $r_0$, can be three-dimensionally (quasi-)stable in some regions of parameters $\Lambda=\ln(R_0/\xi)$ and $W=r_0/R_0$. At fixed $\Lambda$, stable bands on $W$ are intervals between non-overlapping main parametric resonances for different (integer) azimuthal wave numbers $m$. The stable intervals are most wide ($\Delta W\sim$ 0.01--0.05) between $m$-pairs $(1,2)$ and $(2,3)$ at $\Lambda\approx$ 4--12 thus corresponding to micro/mesoscopic sizes of vortex rings in the case of superfluid $^4$He. With four and more rings, at least for $W>0.1$, resonances overlap for all $\Lambda$ and no stable domains exist.

## About application for FRBF-a grant

14 September 2018 in 11:30 (short)

S.S. Vergeles

Report on application for RFBR-a grant. The project topic is "Theory elaboration for coherent vortices in a three-dimensional fluid."

## Synchronization of Conservative Parallel Discrete Event Simulations on a Small-World Network

7 September 2018 in 11:30

Lev N. Shchur и Liliia Ziganurova

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations (PDES). We build a model of the evolution of local virtual times (LVT) in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar–Parisi–Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.
L. Ziganurova, L.N. Shchur, Synchronization of Conservative Parallel Discrete Event Simulations on a Small-World Network, Phys. Rev. E 98, 022218 (2018); arXiv:1807.04463

## Quantum Many-Body Physics of Qubits

22 June 2018 in 11:30

L. Glazman (Yale University)

The ongoing development of superconducting qubits has brought some basic questions of many-body physics to the research forefront, and in some cases helped solving them. I will address two effects in quantum condensed matter highlighted by the development of a fluxonium qubit. The first one is the so-called cosine-phi problem stemming from the seminal paper of Brian Josephson: the predicted there phase dependence of the dissipative current across a Josephson junction was observed in a fluxonium, after nearly 50 years of unsuccessful attempts by other techniques. The second one is the dynamics of a weakly-pinned charge density wave: we predict that the dynamics may be revealed in measurements of microwave reflection off a superinductor, which is a key element of the fluxonium.

## Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion

8 June 2018 in 11:30

A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov and V. E. Zakharov

We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. We admit a presence of gravity forces and surface tension. A time-dependent conformal mapping z(w,t) of the lower complex half-plane of the variable w into the area filled with fluid is performed with the real line of w mapped into the free fluid's surface. We study the dynamics of singularities of both z(w,t) and the complex fluid potential Pi(w,t) in the upper complex half-plane of w. We show the existence of solutions with an arbitrary finite number N of simple complex poles in z_w(w,t) and Pi_w(w,t) which are the derivatives of z(w,t) and Pi(w,t) over w. These poles are often coupled with branch points located at other points of the upper half-plane of w. We find that the residues of the simple poles of z_w(w,t) are new, previously unknown constants of motion, provided surface tension is zero. All these constants of motion commute with each other in the sense of underlying Hamiltonian dynamics. In absence of both gravity and surface tension, the residues of simple poles of Pi_w(w,t) are also the constants of motion. For nonzero gravity and zero surface tension, the residues of poles of any order of Pi_w(w,t) are the trivial linear functions of time. Nonzero surface tension allows residues of poles of even order to be compatible with the fluid dynamics. We also found solutions with N higher order poles. In all above cases the number of independent real integrals of motion is 4N for zero gravity and 4N-1 for nonzero gravity. We suggest that the existence of these nontrivial constants of motion provides an argument in support of the conjecture of complete integrability of free surface hydrodynamics in deep water.
A.I. Dyachenko, S.A. Dyachenko, P.M. Lushnikov, V.E. Zakharov, Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion, Journal of Fluid Mechanics, submitted (2018); arXiv:1809.09584.

## World population and climate variations

11 May 2018 in 11:30

Alexey Byalko

Few sets of the world population data are analyzed from 1 AD to 2015 together with temperature variations of the North Hemisphere from 1 AD to 1979. Possible data errors are evaluated. Hyperbolical behavior of the world population was evaluated by approximation of its inverse function. The population index is introduced as the relative difference between inverse numerical data and its parabolic approximation. The index occurs to be a bounded and an average zero function with the nearly uniform error level. He describes relative variations of the world population in the past. The population index is compared with North Hemisphere temperature variations. However, the population response to temperature variations occurred with a significant delay of about 100 years. Possible reasons for such a correlation are discussed against the background of known historical events and analyzed by the Hurst method. The historical analysis and the found climate—population correlations give a principal possibility to forecast the world population behavior approximately up to year 2080.

## Eukaryotic cell polarity and protein sorting

27 April 2018 in 11:30

Andrea Gamba, Politecnico di Torino

I will review some of the biophysical processes that allow eukaryotic cells to break their native symmetry and polarize in order to provide adequate responses to signals and properly adapt to the environment. An essential part of the process is the incessant spatial reorganization of membrane-bound proteins due to the action of reinforcing biochemical feedback loops that contrast the homogenizing effect of diffusion. A second component is the coupling of protein and lipid dynamics: protein crowding induces the bending of lipid membranes and the nucleation of small lipid vesicles enriched in specific molecular factors destined to be targeted to appropriate destinations. This mechanism leads to an incessant distillation process controlled by the strength of protein-protein interactions. A phenomenological theory of the process can be developed, predicting the existence of an optimal distillation regime characterized by simple scaling laws. Experiments suggest that living cells work close to this optimal regime, likely as the result of evolutionary pressure.

## Dielectric response of Anderson and pseudogapped insulators

27 April 2018 in 11:30

M.V. Feigel'man, D.A. Ivanov, E. Cuevas

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the Superconductor-Insulator Transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.
M.V. Feigel’man, D.A. Ivanov, E. Cuevas, Dielectric response of Anderson and pseudogapped insulators, New J. Phys. 20, 053045 (2018); arXiv:1711.05972

## Some Aspects of Diquarks as seen by String Theory

20 April 2018 in 11:30

Oleg Andreev

I will discuss a few aspects of diquarks in QCD from the viewpoint of a 5-dimensional effective string theory.

## Magnetic oscillations of in-plane conductivity in quasi-two-dimensional metals

13 April 2018 in 11:30

Pavel Grigor’ev

We develop the theory of transverse magnetoresistance in layered quasi-two-dimensional metals. Using the Kubo formula and harmonic expansion we calculate intralayer conductivity in a magnetic field perpendicular to conducting layers. The analytical expressions for the amplitudes and phases of magnetic quantum oscillations (MQO) and of the so-called slow oscillations (SlO) are derived and applied to analyze their behavior as a function of several parameters: magnetic field strength, interlayer transfer integral and the Landau-level width. Both the MQO and SlO of intralayer and interlayer conductivity have approximately opposite phase in weak magnetic field and the same phase in strong field. The amplitude of SlO of intralayer conductivity changes sign at $\omega_c\tau\approx\sqrt{3}$. There are several other qualitative differences between magnetic oscillations of in-plane and out-of-plane conductivity. The results obtained are useful to analyze experimental data on magnetoresistance oscillations in various strongly anisotropic quasi-2D metals.

## Dynamic phase transition in rare events statistics of 1D KPZ problem

30 March 2018 in 11:30

Alex Kamenev (University of Minnesota)

I will review the concept of non-equilibrium phase transitions in rare events statistics as well as a recent dramatic progress in studies of 1D KPZ. The focus of my talk is on the reflection symmetry breaking phase transition recently found stationary KPZ problem: https://arxiv.org/abs/1606.08738

## Chiral magnetic crystals

23 March 2018 in 11:30

Markus Garst (TU Dresden)

The weak Dzyaloshinskii-Moriya interaction in chiral cubic magnets like MnSi, FeGe or Cu2OSeO3 twists the magnetization on long length scales resulting in spatially periodic magnetic textures — magnetic crystals. There exist especially magnetic crystals with a one- and two-dimensional periodicity corresponding to the magnetic helix and the topologically non-trivial skyrmion lattice, respectively. In this talk, we provide an overview of their properties. In particular, we discuss the crystallization process of these magnetic crystals that is characterized by strongly correlated chiral paramagnons that drive the transition first-order [1,2]. This fluctuation-induced first-order transition is well described by a theory put forward by Brazovskii. We will introduce the magnon band structure and their non-reciprocal properties in the presence of a magnetic field [3,4]. For the skyrmion lattice, this band structure is topological and characterized by finite Chern numbers that can be attributed to the formation of magnon Landau levels due to an emergent orbital magnetic field [5,6,7]. Finally, we will discuss domain walls of helimagnets that share similarities with grain boundaries consisting of disclination and dislocation defects of the helimagnetic order [8]. References: [1] M. Janoschek et al. Phys. Rev. B 87, 134407 (2013). [2] A. Bauer, M. Garst and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013). [3] M. Kugler et al. Phys. Rev. Lett. 115, 097203 (2015) [4] T. Weber et al. arXiv:1708.02098 [5] C. Schütte and M. Garst, Phys. Rev. B 90, 094423 (2014). [6] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015). [7] M. Garst J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017) [8] P. Schoenherr et al. Nat. Phys. in press, arXiv:1704.06288

## Manufacturing of holes in supported films: transition from beam dependent to shock dependent radius of hole as absorbed energy increases

9 February 2018 in 11:30

N. Inogamov, V. Shepelev, P. Danilov, A. Kuchmizhak

Thin films on supporting substrates are important class of laser targets for surface nanomodification for, e.g., plasmonic or sensoric applications. There are many papers devoted to this problem. But all of them are concentrated on dynamics of a film, paying small attention to substrate. In those papers the substrate is just an object absorbing the first shock. Here we present another point of view directed namely onto dynamics of a substrate. We consider (i) generation of a shock wave (SW) in a supporting substrate, (this si generation by impact of a film/support contact on supporting condensed medium); (ii) transition from 1D to 2D propagation of SW; (iii) we analyze lateral propagation of the SW along a film/support contact; and (iv) we calculate pressure in the compressed layer behind the SW decaying with time. This positive pressure acting from substrate to the film accelerates the film in direction to vacuum. Above some threshold, velocity of accelerated film is enough to separate the film from support. In the cases with large energy absorbed by a film, the circle of separation is significantly wider than the circle of high heating around the focal laser spot on film surface. Absorbed laser heat exponentially decays around an irradiated spot $F = Fc\, exp(-r^2/RL^2)$, where RL is radius of laser Gaussian beam. While the law of decay for the 2D SW in substrate is the power law. Therefore in the mentioned cases of powerful laser action, the edge of a separation circle is driven by SW in support.
Illustrative materials are posted on youtube:

Video 1
This movie shows the map of evolution of density field. The gold film is the narrow horizontal strip, "vacuum" is above, supporting substrate is below the strip

Video 2
This is the pressure map. We see two shocks: one above and second below the film. Don't pay attention to the shock above, i.e. to shock in "vacuum", because in our simulation we cannot use real vacuum rho=0, p=0. Therefore we use low density media in place of vacuum. Pay attention to the left and right wings of crescent type shock propagating down. These wings pass along the film. Shock pressure in the wings accelerate the film up thus separating it from the silica substrate.

doc

## Differential Poisson's ratio of a crystalline two-dimensional membrane

26 January 2018 in 11:30

I.S. Burmistrov

We compute analytically the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $\nu = -1/3 + 0.016/d_c + O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.

## Mesoscopic Stoner instability: Suppression by tunneling to a reservoir

19 January 2018 in 11:30

I.S. Burmistrov

We derive the generalized Ambegaokar-Eckern-Schon action which governs the dynamics of the charge and spin degrees of freedom for the quantum dot described by the universal Hamiltonian and tunnel coupled to a reservoir. Contrary to previous works, we derive this dissipative action without the following assumptions (i) the absolute value of the spin is not a ected by the tunneling coupling to a reservoir and (ii) the spin rotates slowly such that the adiabatic approximation holds. We use the derived dissipative action for analysis of stability of the mesoscopic Stoner phenomenon with respect to the electron tunneling to a reservoir. We nd that at nite temperature the electron tunneling suppresses the mesoscopic Stoner instability at tunneling conductance which depends on temperature. At zero temperature we predict the existence of the quantum phase transition between the mesoscopic Stoner phase and the paramagnetic phase.

## Exact solutions for nonlinear development of Kelvin-Helmholtz instability for counterflow of superfluid and normal components of Helium II

22 December 2017 in 11:30

Pavel M. Lushnikov and Nikolay M. Zubarev

A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.

## Helical edge transport in the presence of anisotropic magnetic impurity

17 November 2017 in 11:30

P. D. Kurilovich, V. D. Kurilovich, I. S. Burmistrov, M. Goldstein

We consider the effects of electron scattering on a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance might be a non-monotonous function of the voltage with several extrema. Effects of magnetic anisotropy for the impurity are considered.

## Explicit computation of the Calabi-Yau moduli space geometry

10 November 2017 in 11:30

K. Aleshkin, A. Belavin

Knowledge of the CY moduli space geometry is crucial to determine Low energy Lagranzhian in superstring compactifications. For hypersurfaces in projective spaces explicit computations were done only in a few cases. In the talk I will explain a recently proposed method, which allows to perform explicit computations easily and in the more general cases. I'l show how to apply this method to computation the 101-dimensional moduli space of Quintic threefold .

## Cooper pair splitting in ballistic ferromagnetic SQUIDs

27 October 2017 in 11:30

P.L. Stroganov, Ya.V. Fominov

We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a pi-junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.

## Out-of-equilibrium statistical physics of optimization and learning

13 October 2017 in 11:30

Riccardo Zecchina (Bocconi University)

The extraction of information from large amounts of data is one of the prominent cross disciplinary challenges in contemporary science. Solving optimization and learning problems over large scale data sets requires the design of efficient algorithms over very large scale networks of constraints. These problems can be viewed as minimization problems over very complex energy landscapes, for which out-of-equilibrium phenomena of the type studied in statistical physics of disordered systems often play a crucial role. In this talk I will give a brief overview of the main conceptual advances, and I will discuss some recent results which provide both sharp predictions on the theory underlying the most advanced Machine Learning techniques and novel algorithms. I will conclude by describing a serendipitous mathematical connection between the novel algorithms and quantum annealing, and I will give concrete examples of quantum vs thermal exponential speed up.

## Paraconductivity of pseudogapped superconductors

6 October 2017 in 11:30

Igor Poboiko and Mikhail Feigel'man

We calculate Aslamazov-Larkin paraconductity for a model of strongly disordered superconductors (dimensions d=2,3) with a large pseudogap whose magnitude strongly exceeds transition temperature Tc. We show that, within Gaussian approximation over Cooper-pair fluctuations, paraconductivity is just twice larger that the classical AL result at the same ε = (T-Tc)/Tc. Upon decreasing ε, Gaussian approximation is violated due to local fluctuations of pairing fields that become relevant at ε < ε1 « 1. Characteristic scale ε1 is much larger than the width ε2 of the thermodynamical critical region, that is determined via the Ginzburg criterion, ε2 ≈ ε1d. We argue that in the intermediate region ε2 < ε < ε1 paraconductivity follows the same AL power law, albeit with another (yet unknown) numerical prefactor. At further decrease of the temperature, all kinds of fluctuational corrections become strong at ε < ε2; in particular, conductivity occurs to be strongly inhomogenuous in real space.

## On Heavy Quarks in the Quark-Gluon Plasma and String Theory

15 September 2017 in 11:30

Oleg Andreev

I will discuss two issues related to heavy quarks in the strongly coupled quark gluon plasma from the string theory viewpoint. I begin with the expectation value of the Polyakov loop in the deconfined phase or, equivalently, the heavy quark free energy at finite temperature. Then, I continue with the relation between the drag force coefficient and the spatial string tension.

## New Kaluza-Klein Instantons and Decay of AdS Vacua

8 September 2017 in 11:30

Lev Spodyneiko

We construct a generalization of Witten’s Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten’s instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit instability of non-supersymmetric AdS5 vacua in M Theory compactified on positive Kahler-Einstein spaces, providing a further evidence for the recent conjecture that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.

## Transport in a disordered ν=2/3 fractional quantum Hall junction

23 June 2017 in 11:30

Ivan Protopopov

Electric and thermal transport properties of a ν=2/3 fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, G and G_Q, with system size L and temperature T. This is done both for the case of strong interaction between the 1 and 1/3 modes (when the low-temperature physics of the interacting segment of the device is controlled by the vicinity of the strong-disorder Kane-Fisher-Polchinski fixed point) and for relatively weak interaction, for which the disorder is irrelevant at T=0 in the renormalization-group sense. The transport properties in both cases are similar in several respects. In particular, G(L) is close to 4/3 (in units of e2/h) and G_Q to 2 (in units of πT/6ℏ) for small L, independently of the interaction strength. For large L the system is in an incoherent regime, with G given by 2/3 and GQ showing the Ohmic scaling, G_Q\sim 1/L, again for any interaction strength. The hallmark of the strong-disorder fixed point is the emergence of an intermediate range of L, in which the electric conductance shows strong mesoscopic fluctuations and the thermal conductance is G_Q=1. The analysis is extended also to a device with floating 1/3 mode, as studied in a recent experiment [A. Grivnin et al, Phys. Rev. Lett. 113, 266803 (2014)].

## Domains, switching and negative capacitance in nano-scale ferroelectrics

19 May 2017 in 11:30

Igor Lukyanchuk

Formation of unusual textures of polarization is imminent for nano-scale ferroelectric samples, films, rods, and granules, where the depolarization surface effects play the crucial role. We consider the unconventional topological polarization textures in several nano-scale systems, in which they were either already directly observed or can be yet discovered. Polarization domains that alternate the surface charge distribution, first proposed by Landau (1935) in contents of ferromagnetism can be formed in ferroelectric thin films as an effective mechanism to confine the depolarization field to the near-surface layer and diminish the depolarization energy. Very recently we have demonstrated that the few-nanometer thick ferroelectric/paraelectric superlattices with periodic domain structures exhibit the striking feature. The effective capacitance of ferroelectric layers is negative. This effect is explained by the opposite orientation of the depolarizing field with respect to the field-induced averaged polarization. Moreover, in sub-THz region the real part of the dielectric constant becomes positive, passing through zero at frequency ~0.3-3THz, inducing the resonance effect, suitable for the design of the ultra-small low-energy THz chips. Multi-vortex and skyrmion states are formed inside ferroelectric cylindrical nano-dots and nanorods to reduce the depolarization energy. We study the stability of such states and calculate the phase diagram of the system. We demonstrate that the topological class of the most stable topological excitations can be driven by the geometrical and electrical parameters of the system, external field, and temperature. We target the multi-domain and topological excitations in FE nanodots as a platform for multivalued logic units, for neuromorphic computing.

## Some new results on Belief Propagation, Loop Calculus, Sampling and Gauge Transformations

14 April 2017 in 11:30

M. Chertkov (Skoltech + on leave from LANL)

In this talk I plan to review recent progress made in constructing practical algorithms for computing partition function of a general loopy graphical model. After some introductory material, setting up notations and explaining the Loop Calculus approach (Chertkov, Chernyak 2006), I will turn to explaining new results on 1) constructing Markov Chain which allows to sample from the Loop Series built around a Belief Propagation solution (based on "MCMC assisted by Belief Propagation", https://arxiv.org/abs/1605.09042); 2) exploring gauge freedom beyond Belief Propagation (based on "Gauge Optimization via ADMM for Approximate Inference", https://arxiv.org/abs/1703.01056)

## Wave breaking and soliton turbulence of water waves

24 March 2017 in 11:30

A. Dyachenko and D. Kachulin

We study numerically soliton turbulence at the surface of deep water. One of the main problem here is wave breaking that happens from time to time. We propose a model to take it into account.

## Magnetic disorder in superconductors: Enhancement by mesoscopic fluctuations

17 March 2017 in 11:30

I.S. Burmistrov, M.A. Skvortsov

We study the density of states (DOS) and the transition temperature Tc in a dirty superconducting film with rare classical magnetic impurities of an arbitrary strength described by the Poissonian statistics. We take into account that the potential disorder is a source for mesoscopic fluctuations of the local DOS, and, consequently, for the effective strength of magnetic impurities. We find that these mesoscopic fluctuations result in a non-zero DOS for all energies in the region of the phase diagram where without this effect the DOS is zero within the standard mean-field theory. This mechanism can be more efficient in filling the mean-field superconducting gap than rare fluctuations of the potential disorder (instantons). Depending on the magnetic impurity strength, the suppression of Tc by spin-flip scattering can be faster or slower than in the standard mean-field theory.

## Entanglement entropy and particle number cumulants of disordered fermions

10 February 2017 in 11:30

I.S Burmistrov

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

## Vzaimovliyanie kulonovskoi blokady, ferroelektrichestva i elektronnogo transporta v mezoskopicheskikh nanostrukturakh

23 December 2016 in 11:30

N.M. Shchelkachev

We investigate the interplay of ferroelectricity and quantum electron transport at the nanoscale in the regime of Coulomb blockade. Ferroelectric polarization in this case is no longer the external parameter but should be self-consistently calculated along with electron hopping probabilities leading to new physical transport phenomena.

## Skyrmion Dynamics in Ferromagnets and Antiferromagnets

25 November 2016 in 11:30

Oleg Tretiakov (Tohoku University, Japan)

Manipulating small spin textures that can serve as bits of information by electric and spin currents is one of the main challenges in the field of spintronics. Ferromagnetic skyrmions recently attracted a lot of attention because they are small in size and are better than domain walls at avoiding pinning sites while moved by electric current. Nevertheless, ferromagnetic skyrmions also have certain disadvantages, such as the presence of stray fields and transverse dynamics, making them harder to employ in spintronic devices. To avoid these unwanted effects, we propose a novel topological object: the antiferromagnetic (AFM) skyrmion and explore its properties using analytical theory based on generalized Thiele equation and micromagnetic simulations. This topological texture has no stray fields and we show that its dynamics are faster compared to its ferromagnetic analogue. We obtain the range of stability and the dependence of AFM skyrmion radius on the strength of Dzyaloshinskii-Moriya interaction coming from relativistic spin-orbit effects. Moreover, we study the temperature effects on the stability and mobility of AFM skyrmions. We find that the thermal properties, e.g. such as the antiferromagnetic skyrmion radius and diffusion constant, are rather different from those for ferromagnetic skyrmions. More importantly, we show that due to unusual topology the AFM skyrmions do not have a velocity component transverse to the current (no topological Hall effect), and thus may be interesting candidates for spintronic memory and logic applications.

## On Self-Dual Yang-Mills Theory

18 November 2016 in 11:30

Igor’ Polyubin

We discuss renormalization of the theory and calculate corresponding beta-functions. Also we compute some exact two and three point correlatoion functions and four point (++++) amplitude and check their conformal invariance.

## Two-instanton approximation to the Coulomb blockade problem

14 October 2016 in 11:30

Burmistrov I.S.

We develop the two-instanton approximation to the current-voltage characteristic of a single electron transistor within the Ambegaokar-Eckern-Sch\"on model. We determine the temperature and gate voltage dependence of the Coulomb blockade oscillations of the conductance and the effective charge. We find that a small (in comparison with the charging energy) bias voltage leads to significant suppression of the Coulomb blockade oscillations and to appearance of the bias-dependent phase shift.

## Weakly Nonlinear Nonlocal Equation for Envelope of Water Waves

14 October 2016 in 11:30

A.I. Dyachenko

For deep water waves the equation for the envelope is derived. The equation is nonlocal. The assumption of a narrowness of spectral band around a characteristic wave is not is necessary. Thus, this equation is suitable for description of extreme waves (freak waves).

## Analogous black-holes in Bose-Einstein condensates: how to create them and how to detect the associated (sonic) Hawking radiation ?

7 October 2016 in 11:30

Nicolas Pavloff, LPTMS (Orsay)

A "dumb hole" is the sonic equivalent of a black hole: it is a stationary flow pattern in which the downstream flow is supersonic whereas the upstream one is subsonic (as in a de Laval nozzle). In 1981, Unruh suggested that dumb holes should emit a sonic radiation analogous to the celebrated Hawking radiation of black holes.
I shall first present realistic realizations of a sonic event horizon in a 1D Bose-Einstein condensate. In a second stage I will discuss possible (quantum and classical) signatures of the sonic analogous of Hawking radiation in these systems. I will also address the recent experimental results of Steinhauer [Nature Physics (2016)]

## Mesoscopic fluctuations of the single-particle Green's function at Anderson transitions with Coulomb interaction

30 September 2016 in 11:30

Burmistrov I.S.

Using the two-loop analysis and the background field method we demonstrate that the local pure scaling operators without derivatives in the Finkel'stein nonlinear sigma model can be constructed by straightforward generalization of the corresponding operators for the noninteracting case. These pure scaling operators demonstrate multifractal behavior and describe mesoscopic fluctuations of the single-particle Green's function. We determine anomalous dimensions of all such pure scaling operators in the interacting theory within the two-loop approximation.

## Physics at the Edge: A New Paradigm for Shot Noise

16 September 2016 in 11:30

Yuval Gefen (Weizmann Institute of Science)

Questions on the nature of edge reconstruction and ‘where does the current flow’ in the quantum Hall effect (QHE) have been debated for years. Moreover, the recent observation of proliferation of ‘upstream’ neutral modes in the fractional QHE raised doubts about the present models of edge channels. I will focus on the hole-conjugate state \nu=2/3 , and present a new picture of edge reconstruction. For example, while the hitherto accepted model for \nu=2/3 consists of a single downstream charge channel with conductance 2/3 and an upstream neutral mode, it has been recently predicted theoretically and found experimentally that the current is carried by two separate downstream edge channels, each with conductance 1/3 accompanied by upstream neutral mode(s). We find that if the two downstream channels are not equilibrated, inter-mode equilibration (via particle exchange) is accompanied by an excitation of upstream neutral modes. In turn, the counter-propagating neutral modes, moving in close proximity to the charge modes, fragment into propagating charges, inducing thus downstream current fluctuations with zero net current – a novel mechanism for non-equilibrium noise. The latter is shot noise with quantized Fano factors, which does not involve beam partitioning.

## Dynamic correlations in 1D superfluids: the particle-wave duality

9 September 2016 in 11:30

Dimitri M. Gangardt (University of Birmingham)

While phonons are routinely used to describe low-energy properties of quantum superfluids, repulsive bosons in one dimension are special: their low energy excitations allow for an alternative decription in terms of fermionic quasiparticles. In my talk I will present the quasiclassical theory of these excitations which allows calculation of the dynamical structure factor in a generic 1D Bose liquid. In this theory the main role is played by singular kink-like configurations of the bosonic field. I will demonstrate that it is the kinetics of these quasiparticles rather than hydrodynamics which provides an effective description of dynamics of 1D interacting bosons.

## Flat Coordinates on Frobenius Manifolds in the case of the irrelevant deformations

2 September 2016 in 11:30

L. Spodyneiko

We use the suggested recently conjecture about the integral representation for the flat coordinates on Frobenius manifolds connected with isolated singularities to compute the flat coordinates for the deformed Gepner chiral ring SU(3)4 .
We verify this conjecture by comparing expressions for the flat coordinates obtained from the conjecture with one found by direct computation. The considered case of is of particular interest since together with the relevant and marginal deformations it has one irrelevant deformation.

## Closed equations for the jump along branch cut of Stokes wave

17 June 2016 in 11:30

Pavel Lushnikov

2D hydrodynamics of ideal fluid with free surface can be addressed through jump at the branch cuts in the complex plane. The particular example is the Stokes wave which is the nonlinear gravity wave propagating with the constant velocity. The near-limiting Stokes wave is considered which poses a challenge for simulations based on Fourier transform because of the approach of the branch point to the real line in the complex plane. Instead the closed equations on the branch cut are considered. However, numerical quadratures for such equations have extreme ill-conditioning making them impossible to use. Instead the analytical information about jump of the branch cut is used to construct the analytic quadrature significantly suppressing ill-conditioning. It suggest the efficient way to address 2D turbulence of highly nonlinear water waves through the dynamics of branch cuts.

## Josephson-effect in 3DTI and 2DTI based on HgCdTe heterostructures

22 April 2016 in 11:30

Teun Klapwijk (TU Delft)

I will report on experimental results obtained at Molenkamp’s group in Würzburg on ‘missing odd’ Shapiro steps and on emission of Josephson radiation. It is known that as a consequence of the Josephson equations, a strong relation exists between the voltage V measured across a Josephson junction and the characteristic frequency fJ =2eV/h of the current flowing in it. By applying microwave radiation steps occur at integer values of the voltage. Alternatively, ’listening’ to the rf signal radiated by the circulating supercurrent is a passive way of probing its properties. The data provide compelling evidence for the presence of a substantial 4\pi Josephson-current as would be expected from zero-enegry states. The results are available on the arxiv at: arXiv:1603.09611, arXiv:1601.08055, arXiv:1503.05591

Work done by: J.Wiedenmann, E.Bocquillon, R. Deacon, T.M.Klapwijk and various co-authors.
The research is supported by a 2014 Alexander von Humboldt prize.

## Low-energy field theory of disordered Weyl metals.

8 April 2016 in 11:30

Dmitry Bagrets (Institute for Theoretical Physics, University of Cologne, Germany)

In my talk I discuss the transport properties of disordered Weyl semimetals. In these systems, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response -- the anomalous Hall effect (AQHE), and chiral magnetic effect (CME). I will demonstrate how an interplay of symmetry breaking and the chiral anomaly leads to the low-energy field theory containing two types of topological terms --- the Pruisken term describing AQHE and a variant of the non-Abelian Chern-Simons term responsible for CME. I will then discuss the signatures of CME in the magnetoconductance and shot noise assuming a quasi-one-dimensional geometry with a disordered Weyl semimetal nanowire being placed in the contact with two normal leads. An application of the magnetic field B along the nanowire creates the chiral 1d channels propagating parallel to B. They survive disorder averaging and the amount of them equals to the number of flux quanta piercing the nanowire. As the result, the magnetoconductance shows the crossover from quadratic to linear in B behavior while the Fano factor F is exponentially suppressed at high B as compared to F=1/3 at low B.
References: Dmitry Bagrets and Alexander Altland, PRL 114, 257201 (2015); PRB 93, 075113 (2016)

## Fazovye perekhody v geksaticheskikh zhidkikh kristallakh

11 March 2016 in 11:30

Efim Kats

We resolve the old riddle related to the critical behavior of the heat capacity near the smectic A -- hexatic second order phase transition. Experiment suggests a large'' specific heat critical exponent $\alpha=0.5 \div 0.7$ inconsistent with the universality class for this phase transition implying the very small negative exponent $\alpha\approx-0.01$. We show that essential features of the smectic A -- hexatic phase transition can be rationalized in the framework of a theoretical model treating jointly fluctuations of the hexatic orientational and of the positional order parameters. Assuming that the positional (translational) correlation length $\xi_{tr}$ is larger than the hexatic correlation length $\xi_h$, we calculate a temperature dependence of the specific heat in the critical region near the smectic A -- hexatic phase transition. Our results are in a quantitative agreement with the calorimetric experimental data.

## Dynamical phase transitions and statistics of excitations

4 March 2016 in 15:00

Alessandro Silva (SISSA, Trieste)

Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by either a sudden or a gradual change of their parameters. Theoretical examples rage from the behaviour of the O(N) model in the large N limit as well as spin-model with long range interactions, both showing dynamical criticality in their prethermal steady-states. In this talk I will start by discussing the characterization of such dynamical phase transitions based on the statistics of produced excitations. I will focus both on the role of fluctuations as well as on the difference between sudden and gradual changes of the parameters. Finally, I will discuss a second type type of dynamical criticality discussed in the literature, related to the emergence of zeroes in the Loschmidt amplitude, and show that this phenomenon is much less generic and robust than standard dynamical criticality.

## Fermi-Pasta-Ulam recurrence and modulation instability

12 February 2016 in 11:30

E.A. Kuznetsov

For the nonlinear Schrodinger equation (NLSE) we give qualitative arguments to explain the Fermi-Pasta-Ulam (FPU) recurrence which can be considered as a result of the modulation instability (MI) development. All known exact NLS solutions in the form of solitons propagating on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate recovers its form with the same amplitude but a different phase, as soon as solitons leave the area where they were originally. This is the analog of the FPU recurrence for the NLSE. We demonstrate, based on the NLSE integrability, that the FPU recurrence takes place for more general solution, in the form of cnoidal wave. This solution, periodic in space, can be represented as a solitonic lattice which, in one limit, for sufficiently large distance between solitons transforms into one separate soliton solution and, in the opposite limit, into the condensate. The cnoidal wave is also modulationally unstable due to soliton overlapping. In spite of the linear instability existence, at the nonlinear stage the cnoidal wave is shown to recover its form (up to constant shift in space and phase).

## Metal ﬁlm on substrate: Dynamics under action of ultra-short laser pulse

12 February 2016 in 11:30

V A Khokhlov, N A Inogamov, S I Anisimov, V V Zhakhovsky, K V Khishchenko

The movement of metal film placed on glass substrate under action of ultra-short laser pulse is studied with using of two-temperature hydrodynamic calculations. The features of the oscillatory modes of movement of the film on the substrate under the influence of low-energy laser pulses are investigated. Transition from film delamination from the substrate as a whole to break of a film and flying away only a forward layer of a film is tracked at growth of the enclosed energy.

## Collective conductivity, criticality and reconstruction in systems with an infinite permittivity

29 January 2016 in 11:30

Serguei Brazovskii (LPTMS, CNRS & University Paris-Sud & NUST MISiS)

This talk will be devoted to conducting systems with unhindered polar deformations: ferroelectric semiconductors near the critical temperature and charge density waves (CDW) subjected to pinning and junctions constraint. For ferroelectrics, epitomized by Mott insulators in organic stack materials, we shall find access to the critical dynamics, to the creep of domain walls, and to the polarization dumping by solitons. For CDWs, we shall model the reconstruction of their current carrying states in junctions channels via dynamical and static vortex structures. For completeness, we shall recall also old stories of frequency and temperature dependence of the permittivity of CDWs under pinning and Coulomb interactions.
The presented results are based on collaborations with P. Monceau and F. Nad in experiment and with N. Kirova and A. Larkin in theory.

## Anisotropic characteristics of the Kraichnan direct cascade in two-dimensional hydrodynamic turbulence

15 January 2016 in 11:30

E.A. Kuznetsov, E.V. Sereshchenko

Statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192 × 8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential inﬂuence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ∼k-4, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum Ek = CKη2/3k−3, where η is enstrophy ﬂux and the Kraichnan constant CK ≈ 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function which, as for the isotropic turbulence, gives the same scaling with respect to separation length R and η = C3ηR3, but the mean over angles and time C3 diﬀers from its isotropic value.

## Rasshcheplenie kuperovskikh par v ferromagnitnykh skvidakh

25 December 2015 in 13:00

Pavel Ioselevich

We study Josephson junctions between superconductors connected by two parallel ferromagnetic arms. For fully polarised ferromagnets, supercurrent through such a SQUID only flows via Cooper pair splitting between the differently polarised arms. The average current is suppressed, but mesoscopic fluctuations lead to a significant typical current. We calculate this current for the SFS SQUID, as well as for a SQUID with metallic arms with magnetic impurities. The latter shows an h/e periodicity in flux. The current in both systems is of fluctuational origin and is stronger for materials with low conductivity and a low superconducting gap.

## Anomalous Hall effect in weakly disordered ferromagnets

18 December 2015 in 11:30

P. M. Ostrovsky

Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions with weak disorder. In this case, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations. The same mechanism for ordiary electrons with spin-orbit coupling (Bychkov-Rashba model) produces an opposite effect increasing the Hall conductivity. In the conduction band, skew scattering with crossed impurity lines is the only source of the anomalous Hall effect.

## Dynamical phase transitions in electronic systems induced by ultra-fast optical pumping.

4 December 2015 in 11:30

Serguei Brazovskii (LPTMS, CNRS & University Paris-Sud & NUST MISiS)

I shall report on several studies of phase transformations in cooperative electronic systems achieved by means of a femto-second optical pumping. 1. Experiments on charge density waves recovered coherent unharmonic undulations of the order parameter, critical slowing down of the collective mode, and evolution of the particle-hole gap. The numerical modeling reproduced the dynamical phase transition, and the waves emitted by “earthquakes” from in depth annihilation events of topological defects.*) 2. The bistable switching to a “hidden” state has been achieved in a “polaronic Wigner-crystalline Mott insulator” 1T-TaS2. The theory focuses upon evolution of electrons and holes as mobile charge carriers, and the crystallized electrons modifiable by intrinsic defects.*) 3. The special case of resonance optical pumping to excitons is realized in systems with a neutral-ionic ferroelectric transition. The modeling of the quantum-coherent quasi-condensate of excitons interacting with the order parameter recovers the dynamical realization of the “excitonic insulator” state and spacio-temporal patterns with self-focusing, domains segregation, and local dynamical phase transitions.**) ----------------------------------------------------------------------------------------------- *)After collaboration with D. Mihailovic group at the Jozef Stefan Institute, Ljubljana, Slovenia. **) After collaboration with N. Kirova, LPS, University Paris-Sud, Orsay, France.

## Spatial Equation for Water Waves

20 November 2015 in 11:30

A.I. Dyachenko and V.E. Zakharov

We derive spatial Hamiltonian equation for the gravity waves on the deep water. The equation is very suitable for laboratry experiments in a Wave Tank.

## Charge relaxation resistance in the cotunneling regime of multi-channel Coulomb blockade: Violation of Korringa-Shiba relation

13 November 2015 in 11:30

I.S. Burmistrov

We study the low frequency admittance of a small metallic island coupled to a gate electrode and to a massive reservoir via a multi channel tunnel junction. The ac current is caused by a slowly oscillating gate voltage. We focus on the regime of inelastic cotunneling in which the dissipation of energy (the real part of the admittance) is determined by two-electron tunneling with creation of electron-hole pairs on the island. We demonstrate that at finite temperatures but low frequencies the energy dissipation is ohmic whereas at zero temperature it is super-ohmic. We find that (i) the charge relaxation resistance (extracted from the real part of the admittance) is strongly temperature dependent, (ii) the imaginary and real parts of the admittance do not satisfy the Korringa-Shiba relation. At zero temperature the charge relaxation resistance vanishes in agreement with the recent zero temperature analysis [M. Filippone and C. Mora, Phys. Rev. B86, 125311 (2012) and P. Dutt, T. L. Schmidt, C. Mora, and K. Le Hur, Phys. Rev. B 87, 155134 (2013)].

## Exactly solvable models of String Theory and Dubrovin-Saito Flat structures

30 October 2015 in 11:30

A. Belavin, Ya. Kononov

It was shown many years ago for $2d$ topological Conformal field theory and more recently for the non-critical String theory that a number of models of these two types can be exactly solved using their connection with the Frobenius manifold (FM) structure introduced by Dubrovin. More precisely these models are connected with a special case of FMs, so called Saito Frobenius manifolds. In this talk we explore the connection of the models of TCFT and non-critical String theory with SFM. The crucial point for obtaining an explicit expression for the correlators is finding the flat coordinates of SFMs as functions of the parameters of the deformed singularity. We suggest a direct way to find the flat coordinates, using the integral representation for the solutions of Gauss-Manin system connected with the corresponding SFM for a simple singularity. Also, we address the possible generalization of our approach for the models investigated by Gepner models which are ${SU(N)_k}/({SU(N-1)_{k+1} \times U(1)})$ Kazama-Suzuki theories .

## Blossom Belief Propagation: Exact Algorithm for Minimum Weight Perfect Matching

16 October 2015 in 11:30

Michael (Misha) Chertkov (New Mexico Consortium & Skoltech)

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this talk, I describe construction of the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs. This is a joint work with Sungsoo Ahn, Sejun Park and Jinwoo Shin (Korean Institute of Science and Technology).

## Development of high vorticity structures in incompressible 3D Euler equations

9 October 2015 in 15:00

D.S. Agafontsev, A.A. Maylybaev, E.A. Kuznetsov

We present in details our numerical scheme and more of our numerical results, on which our previous talk "Folding of vorticity field as a route to the Kolmogorov spectrum" was based.

## Thermal transport in disordered one-dimensional spin chains

9 October 2015 in 11:30

Igor Poboiko, Mikhail Feigel'man

We study one-dimensional anisotropic XY-Heisenberg spin-1/2 chain with weak random fields hziSzi by means of Jordan-Wigner transformation to spinless Luttinger liquid with disorder and bosonization technique. First we investigate phase diagram of the system in terms of dimensionless disorder γ=⟨h2⟩/J2≪1 and anisotropy parameter Δ=Jz/Jxy and find the range of these parameters where disorder is irrelevant in the infrared limit and spin-spin correlations are described by power laws. Then we use the diagram technique in terms of plasmon excitations to study low-temperature behavior of heat conductivity κ and spin conductivity σ in this power-law phase. The obtained Lorentz number L≡κ/σT differs from the value derived earlier by means of memory function method. We argue also that in the studied region inelastic scattering is strong enough to suppress quantum interference in the low-temperature limit.

## Folding of vorticity field as a route to the Kolmogorov spectrum

2 October 2015 in 11:30

E.A. Kuznetsov, D.S. Agafontsev and A.A. Mailybaev

This work is aimed for understanding nonlinear mechanisms at early stages of turbulence, when the flow is not yet affected by viscosity. Based on numerical simulations of the 3D incompressible Euler equations with generic large-scale initial conditions, we show the exponential growth of vorticity developing as thin pancake structures with the vorticity maximum related to the pancake width by the Kolmogorov-type power law, $\omega_max \sim \ell^{-2/3}$. This self-similar dependence is explained as a consequence of the folding for vorticity field obtained from the asymptotic analysis. We argue that increasing with time number of such structures leads to formation of the Kolmogorov energy spectrum observed numerically in a fully inviscid flow, with no tendency towards finite-time blowup.

## Kvantovyi raspad sverkhtokovogo sostoyaniya i sobstvennaya emkost’ Dzhozefsonovskikh perekhodov za ramkami tunnel’nogo priblizheniya

18 September 2015 in 11:30

Daniil Antonenko

A nondissipative supercurrent state of a Josephson junction is metastable with respect to the formation of a finite-resistance state. This transition is driven by fluctuations, thermal at high temperatures and quantum at low temperatures. We evaluate the life time of such a state due to quantum fluctuations in the limit when the supercurrent is approaching the critical current. The decay probability is determined by the instanton action for the superconducting phase difference across the junction. At low temperatures, dynamics of the phase is massive and is determined by the effective capacitance, which is a sum of the geometric and intrinsic capacitance of the junction. We model the central part of the Josephson junction either by an arbitrary short mesoscopic conductor described by the set of its transmission coefficients, or by a diffusive wire of an arbitrary length. The intrinsic capacitance can generally be estimated as $C_* \sim G/E_g$, where $G$ is the normal-state conductance of the junction and $E_g$ is the proximity minigap in its normal part. The obtained capacitance is sufficiently large to qualitatively explain hysteretic behavior of the current-voltage characteristic even in the absence of overheating.

## Observation of half-quantum vortices in superfluid 3He

18 September 2015 in 11:30

S. Autti, V.V. Dmitriev, V.B. Eltsov, J. Makinen, G.E. Volovik, A.N. Yudin, V.V. Zavjalov

Recently in Kapitza Institute a new phase of the superfluid 3He was reported to exist in the aerogel-like nafen structure - the so-called polar phase. As distinct from the other phases - the chiral superfluid 3He-A with Weyl nodes and the fully gapped topological 3He-B with Dirac nodes on the surface - the polar phase has Dirac nodal line in bulk and dispersionless band of Andreev-Majorana fermions on the surface. Being the spin-triplet superfluid with equal-spin pairing the polar phase can support an exotic object - the half-quantum vortex (HQV). Originally the HQVs have been predicted to exist in the Weyl superfluid 3He-A in 1976, but still they have not been observed there: unfavorable combination of spin-orbit and magnetic anisotropy effects on the orientation of the order parameter did not allow to stabilize these vortices in bulk 3He-A under rotation. In nafen, the nearly parallel aerogel strands pin the orbital part of the order parameter of the polar phase. As a result, if the magnetic field is absent or is oriented parallel to nafen strands, the half-quantum vortices win over the conventional single-quantum vortices.
If HQVs are formed in rotation and then the field is tilted with respect to the strands, one expects that the spin-orbit interaction would induce the formation of the topological solitons between the neighboring HQVs providing the peculiar satellite peak in the NMR spectrum. We used this theoretical prediction to stabilize and identify the HQVs in the Helsinki rotated cryostat. For that we cool down a sample of nafen through transition temperature to the polar phase in rotation up to 2.75 rad/s without magnetic field. Then the field is switched on, and in the tilted field we observe a satellite peak in the NMR spectrum. The dependence of the satellite on the rotation velocity, temperature and the field orientation is in agreement with the predictions. If cool-down occurs with the field applied in the transverse direction, no satellite eak is observed. This demonstrates that the single-quantum vortices are formed instead, which have no NMR signatures. in such arrangement these vortices win over the HQVs as expected.

## On mathematical and computational problems of genomics: from sequencing to population structure

11 September 2015 in 15:00

Vladimir Shchur (Sanger Institute, Cambridge, UK)

Genomics is a young research area in bioinformatics. It has appeared recently due to a significant decrease in the value of DNA sequencing. This drop in sequencing prices led to a rapid growth of the amount of genomic data. Mathematical and computational analysis is of a great importance at all stages of the genomic study: from the identification of variable sites (such as mutations, insertions and deletions) to the study of the population structure. We will discuss what kind of major mathematical and computational problems arise in genomics and will introduce their most basic models and concepts.

## Branch cuts of Stokes wave: numerical and analytical results.

5 June 2015 in 11:30

S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich

Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the constant veloci1ty. Simulations with the quadruple (32 digits) and variable precisions (more than 200 digits) are performed to find Stokes wave with high accuracy and study the Stokes wave approaching its limiting form with 120 degrees angle on the crest. A conformal map is used which maps a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. The Stokes wave is fully characterized by the complex singularities in the upper complex half-plane. These singularities are addressed by rational (Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of Pad\'e approximation to the density of complex poles with the increase of the numerical precision and subsequent increase of the number of approximating poles reveals that the only singularities of Stokes wave are branch cuts. We identified that this singularity is the square-root branch point. That branch cut defines the second sheet of the Riemann surface if we cross the branch cut. Second singularity is also the square-root and located in that second (nonphysical) sheet of the Riemann surface in the lower half-plane. Crossing corresponding branch cut in second sheet one arrives to the third sheet of Riemann surface with another singularity etc. As the nonlinearity increases, all singularities approach the real line forming the classical Stokes solution (limiting Stokes wave) with the branch point of power 2/3.

## Topology of Dirac lines and nexus in graphite

8 May 2015 in 11:30

T.T. Heikkila and G.E. Volovik

We consider the Z_2 topology of the Dirac lines - lines of band intersection - in graphite. Four lines (three with topological charge N_1=1 each and one with N_1=-1) merge near the H-point and annihilate due to summation law 1+1=0. The merging point is similar to the real-space nexus, the analog of Dirac monopole at which the Z_2 strings terminate.

## Giant mesoscopic fluctuations of the elastic cotunneling thermopower of a single-electron transistor

24 April 2015 in 11:30

A. S. Vasenko, Denis M. Basko, F. W. J. Hekking (University Grenoble Alpes, CNRS, LPMMC)

We study the thermoelectric transport of a small metallic island weakly coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime, in the case when the ground state of the system corresponds to an even number of electrons on the island, the main mechanism of electron transport at the lowest temperatures is elastic cotunneling. In this regime, the transport coefficients strongly depend on the realization of the random impurity potential or the shape of the island. Using random-matrix theory, we calculate the thermopower and the thermoelectric kinetic coefficient and study the statistics of their mesoscopic fluctuations in the elastic cotunneling regime. The fluctuations of the thermopower turn out to be much larger than the average value.
[Phys. Rev. B 91, 085310 (2015)]

## Superconductor-insulator transitions: Phase diagram and magnetoresistance

27 March 2015 in 11:30

I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin

Influence of disorder-induced Anderson localization and of electron-electron interaction on superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature Tc, the temperature dependence of the resistivity, the phase diagram, as well as the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. Derived RG equations are valid to the lowest order in disorder but for arbitrary electron-electron interaction strength in particle-hole and Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, both with short-range and with long-range (Coulomb) interaction. In the cases of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity Rc of the order of the quantum resistance Rq = h/4e2. When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below Tc.

## Localization-delocalization transition in the distribution of inertial particles in wall-bounded random flow

13 February 2015 in 11:30

S. Belan, A. Chernykh and G. Falkovich

Turbophoresis is the tendency of particles to migrate in the direction of minima of turbulence intensity (say, a wall). It was recently suggested that the sign of turbophoresis can be actually opposite, so that particles agitated by turbulent fluid fluctuations go away from minima of fluctuations intensity if they are inertial enough. That means localization-delocalization transition upon the change of inertia: particles with small inertia go to a minimum of turbulence, while sufficiently inertial particles escape to infinity. We consider the motion of inertial particles near a wall in the case of inelastic particle-wall collisions. The phase diagram for the transition in the inertia-elasticity plane is found. If the restitution coefficient of particle velocity is smaller than some critical value, then the inelastic collapse occurs: the particles are localized near the wall for any inertia. The theoretical predictions are in a good agreement with the results of direct numerical simulations.

## Landau theory for helical nematic phases

6 February 2015 in 11:30

E.I. Kats and V.V. Lebedev

We propose Landau phenomenology for the phase transition from the conventional nematic into the conical helical orientationally non-uniform structure recently identified in liquid crystals formed by banana''-shaped molecules. The mean field predictions are mostly in agreement with experimental data. Based on the analogy with de Gennes model, we argue that fluctuations of the order parameter turn the transition to the first order phase transition rather than continuous one predicted by the mean-field theory. This conclusion is in agreement with experimental observations. We discuss the new Goldstone mode to be observed in the low-temperature phase.

## Effects of the quark-gluon plasma in pp, pA and AA-collisions

30 January 2015 in 11:30

B.G. Zakharov

I review my recent results on physics of pp, pA and AA collisions at RHIC-LHC energies. In the first part of the talk I discuss the electromagnetic response of the quark-gluon plasma in AA-collisions for a realistic space-time evolution of the plasma fireball. We demonstrate that for a realistic electric conductivity the electromagnetic response of the plasma is in a quantum regime when the induced electric current does not generate a classical electromagnetic field as was assumed previously. It can only lead to a rare emission of single photons. In the second part of my talk I discuss jet quenching in pp and pA collisions in the scenario with formation of a mini quark-gluon plasma. We find a significant suppression effect. For light hadrons at p_{T}\sim 10 GeV we obtained the reduction of the spectra by \sim [20-30,25-35,30-40]% in pp collisions at \sqrt{s}=[0.2, 2.76,7] TeV. We discuss how jet quenching in pp collisions may change the predictions for the nuclear modification factors in AA collisions for light and heavy flavors. We also give predictions for modification of the photon-tagged and inclusive jet fragmentation functions in high multiplicity pp events.

## Wilson fermion doubling phenomenon on irregular lattice: the similarity and difference with the case of regular lattice

16 January 2015 in 11:30

S.N. Vergeles

It is shown that the Wilson fermion doubling phenomenon on irregular lattices (simplicial complexes) does exist. This means that the irregular (not smooth) zero or soft modes exist. The statement is proved on 4 Dimensional lattice by means of the Atiyah-Singer index theorem, then it is extended easily into the cases D < 4. But there is a fundamental difference between doubled quanta on regular and irregular lattices: in the latter case the propagator decreases exponentially. This means that the doubled quanta on irregular lattice are "bad" quasiparticles.

## Effective actions, nonrelativistic diffeomorphism invariance and some applications

16 January 2015 in 11:30

Oleg Andreev

I will discuss certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, examples of invariant effective actions, extended gauge symmetry, Horava-Lifshitz gravity and some applications to the theory of quantum Hall effect.

## Obrashchaya khaos vspyat’

5 December 2014 in 11:30

Борис Файн, Сколковский Институт Науки и Технологий

Понятие "хаос" часто упоминается в контексте основ статистической физики. В то же время, до сих пор не до конца ясно, что называть хаосом в многочастичных квантовых системах. Существует распространённое мнение, что поведение квантовых систем является классически хаотичным в макроскопическом пределе на физически наблюдаемых (т.е. не слишком длинных) временах. В этом докладе будет показано, что, даже в макроскопическом пределе и на физически наблюдаемых временах, типичные неинтегрируемые системы взаимодействущих квантовых спинов не обладают определяющим свойством классического хаоса, а именно, экспоненциальмой чувствительностью к малым возмущениям. Этот результат получен путём сравнения поведения систем классических и квантовых спинов в ответ на неполное обращение спиновой динамики во времени. Такое обращение во времени известно в статистической физике как "Лошмидтовское эхо" и реализуемо методами ядерного магнитного резонанса как "магическое эхо". В последнем случае, отсутствие экспоненциальной чувствительности к малым возмущениям должно быть экспериментально наблюдаемо. [B. V. Fine, T. A. Elsayed, C. M. Kropf, and A. S. de Wijn, Phys. Rev. E 89, 012923 (2014)]

## Density of states in a two-dimensional chiral metal with vacancies

14 November 2014 in 11:30

P. M. Ostrovsky

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to conventional chiral metals. In particular, the average density of states diverges as ρ ~ E-1 |lnE|-3/2 and the correlation length Lc ~ |lnE| in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap resulting in exponentially small tails at low energies.

## Struktura i elektronnyi spektr allotropov fosfora

31 October 2014 in 11:30

L.A. Fal’kovskii

The small difference between the rhombohedral phosphorus lattice ($A$-7 phase) and the simple cubic phase as well as between phosphorene and the cubic structure is used in order to construct their quasiparticle band dispersion. We exploit the Peierls idea of the Brillouin zone doubling/folding, which has been previously employed in consideration of semimetals of the $V$ period and $IV$--$VI$ semiconductors. In the common framework, individual properties of phosphorus allotropes are revealed.

## Torzhestvennoe zasedanie, posvyashchennoe 50-letiyu ITF im. L.D. Landau RAN

17 October 2014 in 11:30

Прграмма будет объявлена дополнительно

## Ambegaokar-Eckern-Schön theory for a collective spin: geometric Langevin noise

10 October 2014 in 11:30

Alexander Shnirman (KIT), Yuval Gefen, Arijit Saha, Igor S. Burmistrov, Mikhail N. Kiselev, Alexander Altland

We consider small ferromagnetic particles or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Sch\"on effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

## Minimalnaya teoriya strun i ee skrytye algebraicheskie struktury

3 October 2014 in 11:30

Alexander Belavin

The aim of this talk is to report about of the computation of the correlation numbers in (p,q) Minimal Liouville gravity (MLG). In this work we conjecture that the Douglas equation is applicable to the Minimal Liouville gravity as well as to Matrix Models of 2D gravity. This conjecture requires the following two questions to be answered: how to choose the desired solution of the Douglas string equation and an appropriate form of the so called resonance transformation from the KdV times to the Liouville coupling constants to satisfy the needed constraints which have to be fulfilled in MLG. In our study, using the connection of the approach to MLG based on the connection of the String equation with the Frobenius manifold structure, we find the necessary solution of the String equation. We also show that this solution together with the suitable choosen resonance transformation lead to the results which are consistent with the main requirements of (p,q) models of MLG (the so called selection rules). It is remarkable that the needed solution of the Douglas equation has a very simple form in the at coordinates on the Frobenious manifold in the general case of (p,q) Minimal Liouville.

## Quantum quenches in the many-body localized phase

26 September 2014 in 11:30

Maksym Serbyn, Z. Papic, Dmitry Abanin

Many-body localized (MBL) systems are characterized by the absence of transport and thermalization, and therefore cannot be described by conventional statistical mechanics. In this talk I will discuss the behaviour of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, the local observables reach stationary, highly non-thermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behaviour distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached), and from the ergodic phase (where relaxation is expected to be exponential). Quench protocols considered in this talk can be naturally implemented in systems of ultra cold atoms in disordered optical lattices, and the behaviour of local observables provides a direct experimental signature of many-body localization. [arXiv:1408.4105; arXiv:1403.0693]

## Coulomb blockade for tunneling through a “long island”

5 September 2014 in 11:30

M.V. Feigelman and A.S. Ioselevich

We consider a Coulomb blockade effects for tunnelling through a piece of wire with large resistance $R\gg 1$. This system can not be treated as a zero-dimensional one, as the dynamics of internal inhomogeneous degrees of freedom is crucial. At moderately high temperatures the linear conductance $G$ of the system is suppressed due to the one-dimensional Coulomb zero bias anomaly effect. At low $T$, besides the standard activational factor, there is an additional $T$-independent (though also exponentially strong!) suppression of $G$. It arises due to the tunnelling evolution of the charge in the wire to the equivipotential distribution. In the intermediate range of $T$ the $G(T)$ dependence is a power law, as in the phenomenological environmental theory. The effective environmental resistance'', entering the power exponent, is found explicitly. It depends on the length of the wire and on the positions of the contacts.

## KINETICS IN DISPERSIVE LUTTINGER LIQUIDS: BOSE-FERMI DUALITY

20 June 2014 in 11:30

Ivan Protopopov

We show that nonequilibrium phenomena in dispersive Luttinger liquids posses remarkable weak-strong coupling duality between bosonic and fermionic descriptions. The duality manifests itself both in the collisionless dynamics of a density pulse (via crossover from essentially free-fermion evolution to hydrodynamics) and in the relaxation of fermionic and bosonic excitations.

## Dynamics of Complex Singularities in Water Waves.

20 June 2014 in 11:30

A.O. Korotkevich and P.M. Lushnikov

Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. We consider Stokes wave in the conformal variables which maps the domain occupied by fluid into the lower complex half-plane. Then Stokes wave can be described through the position and the type of complex singularities in the upper complex half-plane. We identi ed that this singularity is the square-root branch point. We reformulated Stokes wave equation through the integral over jump at the branch cut which provides the efficient way for finding of the explicit form of Stokes wave.

## Quantum theory of a spaser-based nanolaser

23 May 2014 in 11:30

Vladimir M. Parfenyev and Sergey S. Vergeles

We present a quantum theory of a spaser-based nanolaser, under the bad-cavity approximation. We find first- and second-order correlation functions g(1)(t) and g(2)(t) below and above the generation threshold, and obtain the average number of plasmons in the cavity. The latter is shown to be of the order of unity near the generation threshold, where the spectral line narrows considerably. In this case the coherence is preserved in a state of active atoms in contradiction to the good-cavity lasers, where the coherence is preserved in a state of photons. The damped oscillations in g(2)(t) above the generation threshold indicate the unusual character of amplitude fluctuations of polarization and population, which become interconnected in this case. Obtained results allow to understand the fundamental principles of operation of nanolasers.

## FROZEN NANOSTRUCTURES PRODUCED BY ULTRASHORT LASER PULSE

21 February 2014 in 11:30

Khokhlov V.A., Inogamov N.A., Anisimov S.I., Zhakhovsky V.V., Emirov Yu.N., Ashitkov S.I., Komarov P.S., Agranat M.B.

A thin surface layer with high temperature and pressure can be produced by almost isochoric heating with a short enough laser pulse. The stretched molten material is formed during melting and hydrodynamical expansion of this layer. Bubble nucleation and cavitation are initiated if a suciently high tensile stress is generated in the melt. Expansion of the bubble ensemble leads to formation of low-dense foam-like material at later times. However, remarkable elasticity of the foam is retained during long time, leading to slow down of expansion. Meanwhile, very high temperature gradient results in ultrafast cooling of the melt. For the laser intensity below the ablation threshold the foam expansion stops, then starts to shrink and nally freezes into complex solid nanostructures, which are observed experimentally. A comparison of experimental results and molecular dynamics simulation is presented.

## Vibrational Modes in Free Standing Graphene Films

14 February 2014 in 11:30

E.I.Kats and V.V. Lebedev

(submitted to PRB, 2014)

## Novel phases in topological superconducting quantum dots

7 February 2014 in 11:30

Karen Michaeli (Weizmann Inst)

Recent progress in realizing topological superconductors has paved the road to study new physical phenomena resulting from the non-abelian statistics of the Majorana modes they host. A particularly interesting situation arises when Majorana bound states in a closed topological superconducting dot are coupled to external normal leads. In this talk , we will show that interactions with the quantum dot drive the lead electrons into a non-Fermi liquid phase, which can be understood by mapping the problem to a variant of a Kondo system. Interestingly, the non-Fermi liquid states in these systems are more robust than in the conventional two channel Kondo problem. This is because realizations with different numbers of metallic leads are connected to each other by a line of fixed points. We will conclude with a discussion of the experimental consequences of our theory.

## Static and dynamic properties of polarization domains in ferroelectric nanostructures

31 January 2014 in 11:30

Igor Lukyanchuk

Developing of novel technologies of functionalization of nano-size ferroelectric samples emerged the growing interest in exploration of such naturally-formed structures as polarization domains. I will present two recent results concerning the dynamic and static properties of domain self-organization.
The first part of my talk will concern the possible application of the domain structures in emerging technologies of Terahertz-detecting devices. We have studied the dynamical permittivity in ferroelectric nanometricaly-thin films with periodic domain structure, sandwiched between two paraelectric layers. The resulting frequency-dependent permittivity demonstrates collective resonance mode in sub-Terahertz frequency region and Debye-like relaxation behavior at low frequencies.
In the second part of my talk I will consider the study of domain-shape instabilities, recently observed in the ferroelectric polymer PVDF-TrFE films having the lower orthorhombic crystallographic symmetry and demonstrating the hexagonal domain faceting. This effect can arise from purely electrostatic depolarizing forces. We show that in contrast to magnetic bubble shape domains where such type of deformation instability has a predominantly elliptical character, the emergence of more symmetrical circular harmonics is favored in ferroelectrics with high dielectric constant.

## Pressure-balanced stationary mirror structures in an anisotropic plasma

24 January 2014 in 11:30

E.A. Kuznetsov, T. Passot, V.P. Ruban, P.L. Sulem

Based on Grad-Shafranov-like equations, a gyrotropic plasma where the pressures in the static regime are only functions of the amplitude of the local magnetic field is shown to be amenable to a variational principle with a free energy density given by the parallel tension. This approach is used to demonstrate that small-amplitude static holes constructed slightly below the mirror instability threshold identify with lump solitons of KPII equation and turn out to be unstable. It is also shown that regularizing effects such as finite Larmor radius corrections cannot be ignored in the description of large-amplitude mirror structures.

## Seeing quantum mechanics by the naked eye in solid state condensates

22 November 2013 in 11:30

Natalia Berloff, DAMTP, Cambridge and Skoltech

In my talk I will discuss the phenomena observed in, and properties of, microcavity exciton-polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton-polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton-polariton condensates lie somewhere between equilibrium Bose-Einstein condensates and lasers. I discuss the coherence properties of exciton-polariton condensates predicted theoretically and studied experimentally, and the wide variety of spatial structures including quantised vortices, trapped states, states of a quantum harmonic oscillator and other coherent structures.

## Long-range quantum Ising spin glasses at T=0: gapless collective excitations and universality

15 November 2013 in 11:30

Alexei Andreanov (MPG)

We solve the Sherrington-Kirkpatrick spin-glass in a transverse field, concentrating on the regime deep in the quantum glass phase at zero temperature. We find that the quantum glass is gapless everywhere in the quantum glass phase, with an Ohmic spectral function of low energy collective excitations. The physical origin of the latter is explained using an effective potential approach. We obtain the pseudogap in the distribution of local fields and its quantum smearing at small values of transverse fields $\Gamma$. For $\Gamma\ll J$ we find the low frequency spectral function to be independent of $\Gamma$. Like the low-$T$ solution of the classical SK model, the quantum glass is also controlled by a self-similarity of the ultrametric structure of metastable states. The self-similarity is related to the fixed point found in the classical case. We reinterpret these results within the TAP approach.

## Spontaneous breaking of isotropy observed in the electronic transport of rare-earth tritellurides

18 October 2013 in 11:30

P.G. Grigor’ev

We show that the isotropic conductivity in the normal state of rare-earth tritelluride RTe₃ compounds is broken by the occurrence of the unidirectinal charge density wave (CDW) in the conducting (a,c) plane below the Peierls transition temperature. In contrast with quasi-one-dimensional systems, the resistivity anomaly associated with the CDW transition is strong in the direction perpendicular to the CDW wave vector Q (a-axis) and very weak in the CDW wave vector Q direction (c-axis). We explain this result by calculating the electrical conductivity for the electron dispersion with momentum-dependent CDW gap as determined by angle-resolved photoemission spectroscopy (ARPES).

## Local conservation laws, structure of states, and entanglement in the many-body localized phase

20 September 2013 in 11:30

Maksym Serbyn, Z. Papic, Dmitry A. Abanin

In the first part of the talk we address the dynamics in the specific model for the many-body localized (MBL) phase. Recent numerical work revealed a slow, logarithmic in time, growth of the entanglement entropy for initial product states of an XXZ spin chain in a strong random magnetic field. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states.
In the second part of the talk, we build generic framework which allows to understand the dynamics in the MBL phase. We construct a complete set of local integrals of motion that characterize MBL phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported with numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for the non-equilibrium quantum dynamics in the MBL phase. In particular, the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.

## Approximate analytical descriptions of the stationary single-vortex Marangoni convection inside an evaporating sessile droplet of capillary size

6 September 2013 in 11:30

L.Yu. Barash

Three versions of an approximate analytical description of the stationary single vortex Marangoni convection in an axially symmetrical sessile drop of capillary size are studied for arbitrary contact angle and compared with the results of numerical simulations. The first approach is heuristic extension of the well-known lubrication approximation. Two other descriptions are developed and named n\tau- and rz-description. They are free from most of restrictive assumptions of the lubrication approach. For droplets with large contact angles they result in better accuracy compared to the heuristic extension of the lubrication approach, which still gives reasonable results within the accuracy 10-30 per cent. For droplets with small contact angles all three analytical descriptions well agree with the numerical data.

## Zashchita diplomnykh rabot

7 June 2013 in 11:30

приглашаются все желающие

## Fast Melting and Crystallization, Powerful Elastic Shocks, and Surface Nano-structuring Caused by Ultrashort Laser Pulses

12 April 2013 in 11:30

N. Inogamov, V. Zhakhovsky, Yu. Petrov, V. Khokhlov, S. Ashitkov, K. Kishchenko, K. Migdal, D. Ilnitsky, M. Agranat, S. Anisimov, V. Fortov

Ultrafast energy deposition in a thin surface layer of metal target irradiated by femtosecond laser pulse may lead to formation of high-pressure wave which eventually breaks to a shock wave during its propagation into the bulk of target. Due to very high-rate deformation the material response to such ultrashort shock loading can be elastic, even for shock pressures approaching to the ultimate strength of solids. Mechanism of laser-induced generation of such shock waves in metals is studied in this work by means of two-temperature hydrodynamics (2T-HD) and molecular dynamics (MD) simulation techniques. 2T-HD method includes an effect of electron pressure on material motion, and utilizes a model of solid based on quantum density functional theory. The complex processes leading to generation of a shock wave, including 2T electron-ion relaxation, propagation of supersonic electron thermal wave, overheating of the solid and ultrafast homogeneous isochoric melting, and pressure build-up in the heated layer are investigated. The elastic-plastic transformation and respective structures of elastic-plastic shock waves for different laser intensities are discussed. It is demonstrated that the pressure in an elastic precursor is independent on absorbed energy, but it is coupled with pressure at the melting front. It is shown that ultrafast deposition of laser energy ~100 mJ/cm2 results in formation of a nonequilibrium two-temperature state lasting several picoseconds. Due to supersonic propagation of heat into the depth of metal the surface layer of ~100 nm thick is heated, where material gains the internal energy of ~1 eV/atom and melts quickly. Expansion of the heated layer leads to strong tensile stress applying to liquid, which triggers nucleation of bubbles followed by foaming of the melt. As our simulations indicate, the foam-like material at target surface may inflate to a micrometer-sized layer without significant decay of the inter-bubble walls because of the high surface tension of liquid metal. Next, the foam begins to collapse, which produces the complex morphology with configurations like bubbles, jets, mushrooms and other liquid nano-structures. In the meantime the surface temperature drops below the melting point and fast recrystallization initiates freezing of the surface nano-structures. Such nano-structures, including frozen bubbles beneath the recrystallized metal surface, were found in our experiments and simulations.

## Jet quenching in AA-collisions from RHIC to LHC

22 February 2013 in 11:30

B.G. Zakharov

I review my recent results on the nuclear suppression of the hadron spectra in AA-collisions (so called jet quenching) due to final state interaction in the hot QCD matter at RHIC and LHC energies.

## Quantum synchronization

7 December 2012 in 11:30

Юлий Назаров (TU Delft)

We show theoretically the possibility of quantum synchronization of Josephson and Bloch oscillations in a superconducting device. One needs an LC oscillator to achieve exponentially small rate of synchronization errors. The synchronization leads to quantization of transresistance similar to that in (Fractional) Quantum Hall Effect.

## NSR conformal blocks with Ramond fields from AGT correspondence

16 November 2012 in 11:30

A. Belavin, B. Mukhametzhanov

We use AGT correspondence between N = 2 SUSY Yang-Mills theory on R4/Z2 and two-dimensional CFT model with the algebra H \plus sl(2)2 \plus NSR to obtain the explicit expressions for 4-point NSR conformal blocks including Ramond fields in terms of Nekrasov partition functions and correlation functions of sl(2)2 WZW model.

## On the scaling of logarithmic correctrons

26 October 2012 in 11:30

L. Shchur, B. Berche (University Henri Poincare, France) and P. Butera (Univesity Milano-Bicocca, Italy)

We present a solution of the non linear renormalization group equations leading to the leading and subleading singular behaviours of physical quantities (free energy density, correlation length, internal energy, specific heat, magnetization, susceptibility and magetocaloric coefficient) at the critical temperature in a non vanishing magnetic field. The solutions i) lead to exact cancellation of logarithmic corrections in universal amplitude ratios and ii) prove recently proposed relations among logarithmic exponents.

## Higgs bosons, t-quarks and Nambu sum rule

28 September 2012 in 11:30

G. Volovik and M. Zubkov

It may appear that the recently found resonance at MH1 = 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons are composite and that there exists, at least, one more composite Higgs excitation, whose mass MH2 ~ 325 GeV satisfies the Nambu sum rule MH12 + MH22 = 4 MT2, where MT ~ 174 GeV is the t-quark mass. CDF collaboration at Fermi Lab and CMS collaboration at LHC reported a small excess in this region.
In addition, there may appear two charged Higgs particles with masses around 245 GeV, which together also obey the Nambu rule. A certain excess of events in this region has been observed by ATLAS collaboration at LHC. Originally this sum rule was suggested by Nambu in 1985 for the Helium 3 superfluid.
(based on our paper arXiv:1209.0204)

## Rayleigh-Taylor turbulent mixing

7 September 2012 in 11:30

Snezhana I. Abarzhi (The University of Chicago, Chicago, IL, USA)

We observe Rayleigh-Taylor (RT) turbulent mixing while looking at how water flows out from an overturned cup. This process governs a broad variety of natural phenomena from astrophysical to atomistic scales. It influences the formation of the ‘hot spot’ in inertial confinement fusion, drives penetration of stellar ejecta into pulsar wind nebula, dominates energy transport in core-collapse supernova, controls material transformation under high strain rates, and strongly affects the dynamics of shocks and blast waves, as wells as flows in atmosphere and ocean.
It was commonly accepted that Rayleigh-Taylor mixing is a process similar to turbulence in a single fluid or plasma. With this idea in mind, experiments designed experiments at high power laser systems Omega (LLE, Rochester, USA) and NIC (LLNL, Livermore, USA) to reproduce and study astrophysical phenomena, such as supernova explosion, in laboratory plasmas under extreme conditions of high energy density. A laser beam with the giant power of trillions of watts deposited energy onto a tiny target within tens of billionth of a second – the time sufficient for the light to pass only a few meters. The target materials turned into hot and dense plasmas and accelerated at the rate of ten billions of the Earth gravity. The expectation was for a ‘super-turbulence’ to develop yet the plasmas flow exhibited significant degree of order.
We developed and applied the new theoretical concept, the invariance of the rate of momentum loss, to describe the transports of mass, momentum and energy in RT turbulent mixing and to capture its anisotropic, inhomogeneous and statistically unsteady character. It was showed that invariant,scaling and spectral properties of unsteady turbulent mixing differ substantially from those of isotropic and homogeneous turbulence. Rayleigh-Taylor mixing indeed exhibits more order, stronger correlations, weaker fluctuations, and steeper statistical spectra when compared to canonical turbulence. While explaining the experimental observations, these theoretical results have also indicated new approaches for mitigation and control of turbulent mixing processes in inertial confinement fusion, for rational design of experiments for high energy density laboratory astrophysics, and for advancement of numerical simulations

## Co-tunneling current through the two-level quantum dot coupled to magnetic leads: A role of exchange interaction

22 June 2012 in 11:30

A. Sharafutdinov

The cotunneling current through a two-level quantum dot weakly coupled to ferromagnetic leads is studied in the Coulomb blockade regime. The cotunneling current is calculated analytically under simple but realistic assumptions as follows: (i) the quantum dot is described by the universal Hamiltonian, (ii) it is doubly occupied, and (iii) it displays a fast spin relaxation. We find that the dependence of the differential conductance on the bias voltage is significantly affected by the exchange interaction on the quantum dot. In particular, for antiparallel magnetic configurations in the leads, the exchange interaction results in the appearance of interference-type contributions from the inelastic processes to the cotunneling current. Such dependence of the cotunneling current on the tunneling amplitude phases should also occur in multi-level quantum dots weakly coupled to ferromagnetic leads near the mesoscopic Stoner instabilities.

## Beyond log-log scaling of critical collapse of Nonlinear Schrodinger equation

22 June 2012 in 11:30

Pavel Lushnikov

We study the collapse of the nonlinear Schrodinger equation (NLS) in critical case of dimension two. The collapse describes e.g. self-focusing of light in nonlinear Kerr media. The scaling of self-similar solutions near collapse point has (t0-t)1/2 scaling law with the logarithmic modifications of log-log type. We show that the leading order log-log modification occurs for nonrealistic exponentially large amplitudes of light. Instead we derived a new equation for adiabatically slow parameter which determines the system dynamics. Based on that equation we develop a perturbation theory for scaling modifications beyond leading log-log order and perform detailed comparison with simulations.

## Weakly coherent regime of interlayer magnetoresistance

8 June 2012 in 11:30

P.D. Grigor’ev

Abstract: Recently the theory of interlayer magnetoresistance in the strongly anisotropic metals has been proposed (by the author) in the regime, where the interlayer transfer integral of electrons is smaller than the cyclotron energy and Landau level broadening due to disorder [1-3]. It was shown [1,2] that in this “weakly coherent” regime the monotonic part of magnetoresistance has qualitatively different behavior than in the standard theory. The damping of magnetic quantum oscillations and the angular dependence of magnetoresistance were also predicted to strongly change in this regime from the coherent 3D case [1,3]. In the present paper [4] we determine the applicability region of the theory in Refs. [1-3] and perform the detailed comparison with experiment on the field dependence of interlayer magnetoresistance of the pressurized (to the normal state) layered organic metal a-(BEDT-TTF)2KHg(SCN)4. The high quasi-two-dimensional anisotropy, when the interlayer hopping time is shorter than the electron mean-free time and than the cyclotron period, leads to a dimensional crossover and to strong deviations from the conventional three-dimensional theory of magnetoresistance. The monotonic field dependence is found to change from the conventional behavior at low magnetic fields to an anomalous one at high fields. The shape of Landau levels, determined from the damping of magnetic quantum oscillations, changes from Lorentzian to Gaussian. This indicates the change of electron dynamics in the disorder potential from the usual coherent three-dimensional regime to a new regime, which can be referred to as weakly coherent. 1. P.D. Grigoriev, “Weakly incoherent regime of interlayer conductivity in magnetic field”, Phys. Rev. B 83, 245129 (2011). 2. P. D. Grigoriev, “Monotonic growth of interlayer magnetoresistance in strong magnetic field in very anisotropic layered metals”, JETP Lett. 94, 47 (2011). 3. P.D. Grigoriev, “New features of magnetoresistance in the strongly anisotropic layered metals”, Физика низких температур, 37(9-10), 930 (2011). 4. P. D. Grigoriev, M. V. Kartsovnik, W. Biberacher, «Weakly coherent regime of interlayer magnetoresistance in organic metal α-(BEDT-TTF) 2KHg(SCN)4», arXiv:1205.0041.

## Fluctuation conductivity in disordered superconducting films

1 June 2012 in 11:30

Konstantin S. Tikhonov, Georg Schwiete, and Alexander M. Finkel'stein

We study the effect of superconducting fluctuations on the longitudinal and the transverse (Hall) conductivity in homogeneously disordered films. Our calculation is based on the Usadel equation in the real-time formulation. We adjust this approach to derive analytic expressions for the fluctuation corrections in the entire metallic part of the temperature-magnetic field phase diagram, including the effects of both classical and quantum fluctuations. This method allows us to obtain fluctuation corrections in a compact and effective way, establishing a direct connection between phenomenological and microscopic calculations.

## Fluctuoscopy of Superconductors

25 May 2012 in 11:30

A.A. Varlamov (Viale del Politecnico), Andreas Glatz, V.M. Vinokur (MSD ANL)

We derive the exact expressions for the fluctuation conductivity in disordered two dimensional superconductors as a function of temperature and magnetic field in the whole phase diagram above the upper critical field line Hc2(T). Ten diagrams of the first order corrections are grouped in four contributions of the different physical nature. We discuss their hierarchy in different domains of the phase diagram and identify that one responsible for quantum phase transition close to Hc2(0). Focusing on the vicinity of the quantum phase transition near zero temperature we arrive to the conclusion that as the magnetic field approaches the critical field Hc2(0) from above, a peculiar dynamic state consisting of clusters of coherently rotating fluctuation Cooper-pairs forms. We estimate the characteristic size ξQF(H) and lifetime τQF(H) of such clusters and indicate in the corresponding domain of the phase diagram, where such phenomenon can be observed. The derived values ξQF(H) and τQF(H) allow us to reproduce qualitatively the available results for the quantum fluctuation contributions to the in-plane conductivity, magnetization, and the Nernst coefficient.

## Form Factors in the Φ1,2 perturbed minimal models

18 May 2012 in 11:30

Oleg Alekseev

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the Φ1,2 perturbed minimal models.

## Sound modes in non-magnetic dielectrics in a magnetic field

20 April 2012 in 11:30

I.E. Dzyaloshinskii, E.I. Kats

We show how gyro-magnetic phenomena dramatically affect vibrations in non-magnetic solids.

## On the accuracy of the Wang-Landau method

23 March 2012 in 11:30

L.N. Shchur

Wang-Landau method developed for the numerical estimation of the density of states in the system with the discrete energy spectrum. Original algorithm are based on the criterium of the histogram flatness, which in fact are never fulfilled. We found that accuracy may be associated with the properties of the transition matrix. Nevertheless, problem of the convergence to the stationary distribution is still open.

## Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

16 March 2012 in 11:30

M. I. Katsnelson, G. E. Volovik

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED (arXiv:1203.1578v2).

## Commuting vector fields and integrable PDEs of hydrodynamic type in multidimensions (joint work with S. V. Manakov)

2 March 2012 in 11:30

P.M. Santini

After summarizing the main features of the direct and inverse spectral transforms for vector fields, used to solve nonlinear multidimensional PDEs arising as commutation condition for vector fields, we concentrate on the inverse problem, a vector nonlinear Riemann problem (NRP), and i) we present a method to identify a class of exactly solvable NRPs, corresponding to distinguished examples of implicit solutions of the nonlinear PDEs; ii) we construct the longtime behavior of the solutions of such PDEs, studying in detail the analytic aspects of wave breaking in multidimensions. The above theory applies, in particular, to the following celebrated nonlinear PDEs of Mathematical Physics: the dispersionless Kadomtsev-Petviashvili, the heavenly and the dispersionless 2D Toda equations.

## Statistical properties of passive scalar in a random flow with a strong shear component

10 February 2012 in 11:30

I.V. Kolololov, Nguen Than Trung

We study mixing of passive scalar by a chaotic velocity field with a relatively strong regular shear component. We show that the tail of partition distribution function (PDF) of coarse-grained passive scalar field differs qualitatively from the corresponding asymptotics in the case of isotropic flow statistics.

## Rayleigh–Taylor instability in a visco-plastic ﬂuid

20 January 2012 in 11:30

A.Yu. Demianov, A.N. Doludenko, N.A. Inogamov, and E.E. Son

The Rayleigh–Taylor and Richtmyer–Meshkov instabilities of a visco-plastic ﬂuid are discussed. The Bingham model is used as an effective rheological model which takes into account plastic effects. For the purposes of numerical simulation a one-mode disturbance of the contact surface between two ﬂuids is considered. The main goal of this work is to construct numerical 2D and 3D models and to obtain the relationship between yield stress and the development of instability.

## Fluctuation-dissipation theorem for chiral systems in nonequilibrium steady states

23 December 2011 in 11:30

Dmitri Feldman

We consider a three-terminal system with a chiral edge channel connecting the source and drain terminals. Charge can tunnel between the chiral edge and a third terminal. The third terminal is maintained at a different temperature and voltage than the source and drain. We prove a general relation for the current noises detected in the drain and third terminal. It has the same structure as an equilibrium fluctuation-dissipation relation with the nonlinear response in place of the linear conductance. The result applies to a general chiral system and can be useful for detecting “upstream” modes on quantum Hall edges.

## Coherent resonance accumulation of the EDM signal at magnetic storage rings

2 December 2011 in 11:30

W.Morse (BNL), N. Nikolaev, F. Rathmann (IKP FZJ)

Permanent EDM of particles and light nuclei is one of the keys to understanding the origin of CP violation and, eventually, of the baryogenesis in our Universe. We describe some unexpected features of spin dynamics in magnetic storage rings supplemented with radiofrequency electric EDM flippers. We report an evalutaion of the spin decoherence time and a finding of magic energies at which the spin diffusion vanishes.

## Bases in 2d conformal field theory and instanton moduli spaces

25 November 2011 in 11:30

A.A. Belavin, M.A. Bershtein, B.L. Feigin, A.V. Litvinov, G.M. Tarnopolskiy

Part 2

## Bases in 2d conformal field theory and instanton moduli spaces

18 November 2011 in 11:30

A.A. Belavin, M.A. Bershtein, B.L. Feigin, A.V. Litvinov, G.M. Tarnopolskiy

Recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties, one of them is the complete factorization of the coefficients of the operator product expansion. We consider a particular case of the U(r) gauge theory on C2/Zp which corresponds to a certain coset conformal field theory and describe the properties of this basis. We argue that in the case p=2, r=2 there exist different bases. We give an explicit construction of one of them. For another basis we propose the formula for matrix elements.

## Localized Majorana state on a disordered surface of a topological insulator

11 November 2011 in 11:30

P. A.Ioselevich, P. M.Ostrovsky, M. V. Feigel'man

We found density of states on a free surface of disordered topological insulator surrounded by a superconductor, in presense of a single-quantum vortex. The problem is shown to be in the B class of the Altland-Zirnbauer classification. Spatial dependence of the low-energy density of states is found. Tunnel current seen by STM i s calculated as function of the voltage.

## Quantum tops as examples of commuting differential operators

7 October 2011 in 11:30

A.B. Shabat, V.E. Adler, V.G. Marikhin

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.

## Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs.

23 September 2011 in 11:30

Emilio Cuevas, Mikhail Feigel'man , Lev Ioffe and Marc Mezard

Origin of continuous energy spectrum in a large disordered interacting quantum system is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce thermal bath and excitation decay. The important question is what is the driving force and the mechanism of transition(s) between two different types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy level statistics of a system of spins-1/2 with anisotropic exchange interaction and random transverse field. Our results present first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in a class of random spin models. Because these models also describes the physics of superconductor-insulator transition in InO and similar materials our results imply the appearance of novel insulating phases in the vicinity of the transition.

## Bosonic analog of the electron bubble: ground-state and non-ground-state BEC of magnons in superfluid 3He-B

16 September 2011 in 11:30

G. Volovik

Long-lived coherent spin precession of 3He-B observed at temperatures around 0.2 Tc is interpreted to represent Bose-Einstein condensation of spin wave excitations or magnons in a magnetic trap which is formed by the orbital texture of order parameter. When the number of magnons increases, they via spin-orbit interaction exert an orienting influence on the orbital texture. Since the texture is very flexible the potential well produced by texture is crucially modified leading to self-localization of magnon BEC. The scenario of self-localization represents the bosonic analog of formation of the electronic bubble in helium liquids, where an injected electron opens a cavity whose size is determined by a balance between the zero-point energy of the electron and the surface energy of the bubble. In our case the role of the electron wave function is played by the condensate wave function of magnon BEC, while the role of the liquid environment is played by the orbital texture, which is expelled from the bubble due to spin-orbit interaction. The bubble free from texture can be filled either with the magnon condensate in the ground states, or with BEC on any excited level. The BEC in a given excited state is populated and sustained by continuous rf pumping at its specific excitation frequency. On switching off the pumping the magnons from an excited level BEC drop to the ground state BEC.

## Motion of near-spherical micro-capsule in planar external flow

9 September 2011 in 11:30

S.S. Vergeles and P.E. Vorobev

Dynamics of a micro-capsule with compressible membrane placed into planar flow is considered. The form of the capsule is assumed to be near-spherical and the membrane forces are calculated in the first order in respect to the membrane displacement. We have established that the capsule dynamics is governed by two dimensionless parameters in this limit, which account for membrane stretch nodulus, viscosities if inner fluid and solvent, capsule radius, external flow gradient and Taylor deformation parameter at rest. Phase diagram for capsule dynamical regimes is plotted on the plane of these two dimensionless parameters in the limits of high and low viscosity contrasts between the fluid inside the capsule and the solvent.

## Magnetic-field-driven quantum phase transitions in unconventional Josephson arrays

2 September 2011 in 11:30

Joshua Paramanandam, Matthew Bell, and Michael Gershenson (Rutgers University, USA)

Arrays of nanoscale Josephson junctions represent an important tool in the exploration of several fundamental problems of the physics of quantum disordered systems, including quantum phase transitions in systems with and without long-range interactions, emergent glassy behavior, and formation of topological phases. The fabrication of novel types of Josephson arrays with unconventional geometries is required to address these issues. We report on the study of low-temperature transport in the arrays with a large number of nearest-neighbor elements. Both linear and non-linear effects in such arrays will be discussed, including the superconductor-insulator transition, an activation transport in the insulating regime, and the threshold for dissipative transport.

## Logarithmic scaling of the critical collapse of Keller-Segel equation

24 June 2011 in 11:30

Pavel Lushnikov

Keller-Segel equation (KS) is a parabolic-elliptic system of partial differential equations with applications to bacterial aggregation and collapse of self-gravitating gas of brownian particles. KS has striking qualitative similarities with nonlinear Schrodinger equation including critical collapse (finite time point-wise singularity) in two dimensions and supercritical collapse in three dimensions. The self-similar solutions near blow up point are studied for KS in critical case together with time dependence of these solutions and their stability. We found logarithmic-type modifications to (t0-t)1/2 scaling law of self-similar solution in qualitative analogy with log-log corrections for NLS. Very good agreement is achieved between the direct numerical simulations of KS with the analytical results by developing a perturbation theory for logarithmic-type modifications. It suggests that log-log corrections in NLS also could be verified in a similar way.

## Topological bound states in 3D media with Weyl points: 1D flat band on the vortex axis and Fermi arc on the surface

3 June 2011 in 11:30

G. Volovik

Topological semimetals first discussed by Abrikosov and Beneslavskii ("Possible existence of substances intermediate between metals and dielectrics", JETP 32 (1971) 699-708) have topologically protected point nodes. Close to that points, electrons behave as Weyl fermions. Later it became clear that the same Weyl points exist in superfluid 3He-A and in the vacuum of Standard model. As in topological insulators, in the topological systems with Weyl fermions there is the bulk-surface and the bulk-vortex correspondence. Due to bulk-vortex correspondence, the core of the 3He-A vortex contains the 1D flat band first found by Kopnin in 1991. The end points of this flat band are determined by projections of the Weyl points to the vortex axis. Due to bulk-surface correspondence, the surface of 3He-A and of 3D topological semimetals contains the Fermi arc - the 1D Fermi line in the 2D momentum space at which fermions have zero energy. The end points of the Fermi arc are determined by projections of the Weyl points to the surface.

## On a discrete analog of the Tzitzeica equation

29 April 2011 in 11:30

An integrable discrete analog of the Tzitzeica equation is found in the form of a partial difference equation on the square grid. Its higher continuous symmetry is an inhomogeneous Volterra-Narita-Bogoyavlensky type lattice equation. It defines a discretization of the Sawada-Kotera equation (KdV-like equation of 5-th order). The integrability of these discretizations is proven by construction of the Lax representations. From the geometric point of view, the Lax representation is a discrete version of Gauss equations for affine spheres. The bilinear equations for the tau-function are derived.

## Hopping conductance in the presence of electro-magnetic fields

22 April 2011 in 11:30

When exposed to sufficiently strong electro-magnetic (EM) fields, the conductance of hopping systems is enhanced. Data taken on six different hopping systems will be shown to illustrate that in the microwaves (MW) regime, the excess conductance is sub-linear with the EM power. It can be demonstrated that the effect is not due to heating. The mechanism for the conductance enhancement will be presented and the implications to some general features of Anderson insulators will be discussed.

ppt

## Form Factors in the Ising Model in Magnetic Field at T=Tc

15 April 2011 in 11:30

Oleg Alekseev

We consider the scaling limit of the two-dimensional Ising Model in a Magnetic Field at T=Tc (IMMF). This model is known to be an integrable QFT whose spectrum and the exact S-matrix is described by the E8 scattering theory. The correlation functions of local operators can be computed within the Form Factor approach. Using the remarkable connection between the IMMF and the Bullough-Dodd model in the framework of the free field representation we obtain exact form factors of local operators in the IMMF. We obtain the recurrent relation which establishes relation between form factors with a different number of particles and provides a convenient procedure for explicit evaluation of the form factors.

## Nepreryvnaya interpolyatsiya mezhdu frustrirovannym Izingom i kvantovymi dimernymi modelyami

8 April 2011 in 11:30

S.E. Korshunov

We propose a new quantum model interpolating between the fully frustrated spin 1/2 Ising model in a transverse field and a dimer model. This model contains a resonating-valence-bond phase, including a line with an exactly solvable ground state of the Rokhsar-Kivelson type. We discuss the phase diagrams of this model on the square and triangular (in terms of the dimer representation) lattices [D. A. Ivanov and S. E. Korshunov, arXiv:1102.1912].

## Nodal topological matter and flat bands

1 April 2011 in 11:30

G.E. Volovik

Topological media are systems whose properties are protected by topology and thus are robust to different perturbations of the system including as the change of the parameters of interaction. In topological insulators, and in the nodeless topological superconductors and superfluids the bulk-surface and bulk-vortex correspondence gives rise to the gapless Dirac or Majorana fermions on the surface of the system or inside the vortex core. In gapless topological media, the bulk-surface and bulk-vortex correspondence is even more interesting: it produces topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Dirac points, such as superfluid 3He-A. Flat band has an extremely singular density of states. This property may give rise in particular to surface superconductivity with an unusually high transition temperature thus opening a possible route for room temperature superconductivity.

## Elastic-plastic phenomena and propagetion of strong shock wawes under the acion of femtosecond laser pulses

18 March 2011 in 11:30

V.A. Khokhlov, N.A. Inogamov, V.V. Zhakhovskii

The splitting of the shock wave (SW) on the elastic precursor and a plastic wave — a characteristic phenomenon that appears only in solid media. Recently, numerical calculations and femtosecond laser experiment revealed the existence of an elastic shock wave at pressure p ~ 10 GPa, 1-2 orders of magnitude greater than the dynamic elastic limit .In these ultra-short waves is not enough time to form a plastic shock wave. In this paper we analyzed the formation and propagation of elastic and plastic waves in aluminum at still higher pressures, obtained with femtosecond lasers. It is found that the elastic precursor survives even in circumstances where the pressure after a plastic front comes up huge quantities p ~ 1 Mbar, at which the melting of the metal. It is shown that the account of superelasticity is required for proper interpretation of the previous laser experiments.

## Ablation of lithium fluoride dielectric crystal by the short pulses of x-ray plasma laser and extreme ultraviolet free electron laser.

18 March 2011 in 11:30

Anisimov S.I., Faenov A.Yu., Inogamov N.A., Khokhlov V.A., Petrov Yu.V., Skobelev I.Yu., Zhakhovskii V.V.

We presented experimental and theoretical studies of ablation of condensed matter by extreme ultraviolet (EUV) and X-ray lasers (XRL). Results obtained by the use of two different soft XRL are compared. The ﬁrst XRL is the collision Ag-plasma laser with pulse duration 7 ps and laser photon energy 89.3 eV, while the second one is EUV free electron laser (EUV-FEL) with pulse duration 0.3 ps and energy of photon 20.2 eV. Investigation of interaction of irradiation from these two types of XRL with the wide gap lithium ﬂuoride (LiF) dielectric shows that ablation thresholds in both cases are approximately the same. Ablation threshold for XRL interacting with dielectric appears to be signiﬁcantly lower than the threshold of ablation when ultrashort laser pulse of optical frequency range interacts with the metal surface. The similarity between the two XRL is due to the short pulse durations of both XRL. They are shorter than, or comparable with the acoustic time, which is necessary for sound to travel through an attenuation depth. These short pulses create thermomechanical stresses which are the reason for spallative ablation in the dielectric as well as it takes place in metals. Thermomechanics and negative pressure deﬁne character of ablation at relatively low ﬂuences of the order of ablation threshold. At such ﬂuences, heating is moderate and matter remains in condensed state where cohesive properties are dynamically important. At higher ﬂuences, XRL transfers the heated layer into the gaseous state where cohesion phenomenon is not signiﬁcant. A theory presented explains a slow growth of ablated mass with a ﬂuence when the short X-ray laser irradiation interacts with the dielectric target as a result of transition from the spallative ablation near threshold value of a ﬂuence to the evaporative ablation at high ﬂuences.

## Magneto-optics of graphite in quantizing magnetic fields

11 March 2011 in 11:30

L.A. Falkovsky

The optical conductivity of graphite in quantizing magnetic fields is analytically evaluated applying the Slonczewski–Weiss–McClure model with the trigonal warping including in the Hamiltonian. Both the dynamical conductivities, longitudinal as well as Hall's, are calculated. The conductivity peaks are explained in terms of the electron transitions in graphite. The conductivities describe the absorption and the Kerr rotation.

## Enhancement of superconductivity by Anderson localization

4 March 2011 in 11:30

I.S. Burmistrov

Influence of disorder on the temperature of superconducting transition (Tc) is studied within the sigma-model renormalization group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short-range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes the Anderson localization leads to strong enhancement of Tc related to the multifractal character of wave functions.

## Quantum Abacus for counting and factorizing numbers

4 March 2011 in 11:30

M. V. Suslov, G. B. Lesovik, G. Blatter

We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base 2, base 3, or base d representation. In operating the algorithm, the number n < N = d^K is read into a K-qudit register through its interaction with a stream of n particles passing in a nearby wire; this step corresponds to a quantum Fourier transformation from the Hilbert space of particles to the Hilbert space of qudit states. An inverse quantum Fourier transformation provides the number n in the base d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semi-classical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows to find the powers of 2, 3, and other primes d in the number n. We show, that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter's performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure a voltage (analog to digital converter) and a simple procedure to entangle multi-particle states. ( arXiv:1011.3646 )

## Fazovaya diagramma frustrirovannoi modeli Izinga s poperechnym magnitnym polem i sotovoi reshyotkoi

18 February 2011 in 11:30

C. E. Korshunov

Motivated by the current interest in the quantum dimer model on the triangular lattice, we investigate the phase diagram of the closely related fully-frustrated transverse field Ising model on the honeycomb lattice using classical and semi-classical approximations. We show that, in addition to the fully polarized phase at large field, the classical model possesses a multitude of phases that break the translational symmetry which, in the dimer language, correspond to a plaquette phase and a columnar phase separated by an infinite cascade of mixed phases. The modification of the phase diagram by quantum fluctuations has been investigated in the context of linear spin-wave theory.

## Rezonansy v modelyakh sh- i sin-Gordona i vysshie uravneniya dvizheniya v teorii Liuvillya

11 February 2011 in 11:30

Mikhail Lashkevich

Высшие уравнения движения в квантовой теории поля Лиувилля, предложенные Ал. Замолодчиковым, интерпретированы как резонансы в конформной теории возмущений от модели свободного безмассового поля. Оператор, отвечающий нуль-вектору в представлении конформной алгебры, находится в резонансе с одним из экспоненциальных операторов. Под резонансом подразумевается ситуация, когда при определенных соотношениях между конформными размерностями полей возникают логарифмические ультрафиолетовые расходимости во всех корреляционных функциях определенных операторов, что приводит к неоднозначной перенормировке этих операторов. Показано, что аналогичные резонансы возникают в модели sh-Гордона, которую можно рассматривать и как возмущение свободного безмассового поля, и как возмущение теории Лиувилля. Точный вид резонанса можно установить, используя результат Ал. Замолодчикова. Структура резонансов в теории sin-Гордона осложняется полюсами в вакуумных средних, отвечающих резонансам между самими экспоненциальными операторами, что приводит к более сложным расходимостям для "нуль-векторов".

## On combinatorial expansion of the conformal blocks arising from AGT conjecture

4 February 2011 in 11:30

Alexey Litvinov

In my talk I will report on our studying of the origin of combinatorial expansion of the conformal blocks suggested by Alday, Gaiotto and Tachikawa. We consider the algebra A, which is the tensor product of commuting with each other Virasoro and Heisenberg algebras and discover the special orthogonal basis of states in the highest weight representations of A. The matrix elements of primary fields in this basis have a very simple factorized form and coincide with the function called Zbif appearing in the instanton counting literature. Having such a simple basis the problem of computation of the conformal blocks simplifies drastically and can be shown to lead to the expansion proposed by AGT. We found that this basis diagonalizes an infinite system of commuting Integrals of Motion related with some integrable hierarchy

## Applying dissipative dynamical systems to pseudorandom number generation: equidistribution property and statistical independence of bits on length up to logarithm of mesh size. RNGSSELIB: Program library for Random Number Generation.

28 January 2011 in 11:30

L.Yu. Barash, L.N. Shchur

The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. New algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, including proofs of periodic properties and of statistical independence of bits on length up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators. The library RNGSSELIB for random number generators (RNGs) based upon the SSE2 command set is presented. The library contains realization of a number of modern and most reliable generators. Usage of SSE2 command set allows to substantially improve performance of the generators. Three new RNG realizations are also constructed. We present detailed analysis of the speed depending on compiler usage and associated optimization level, as well as results of extensive statistical testing for all generators using available test packages. Fast SSE implementations produce exactly the same output sequence as the original algorithms.

## Three approaches to the 2d Quantum gravity

29 October 2010 in 11:30

A. Belavin, M. Bershtein, G. Tarnopolsky

The one-matrix model in the $p$-critical point is considered. We found an explicit expression for the genus 2 free energy. Also we discuss its relation to the Topological gravity. We explain that the free energy of the $p$-critical Matrix model is an analytic continuation of the generating function of the Topological gravity. We check the topological recursion relations for correlation functions in the $p$-critical Matrix model.

## Sverkhmassivnaya chernaya dyra v ellipticheskoi galaktike: akkretsiya goryachego gaza s malym, no konechnym uglovym momentom

22 October 2010 in 11:30

N.A. Inogamov, R.A. Syunyaev

## Scaling and front dynamics in Ising quantum chains

18 November 2005 in 11:30

Dragi Karevski (University Henri Poincare, Nancy, France)

We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a situation where all the spins are hermalized independently, and for the two-temperatures initial state, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb.

## Mesoscopic wave turbulence

2 September 2005 in 11:30

V.E. Zakharov, A.O. Korotkevich, A.N. Pushkarev, A.I. Dyachenko

We report results of sumulation of wave turbulence. Both inverse and direct cascades are observed. The definition of "mesoscopic turbulence" is given. This is a regime when number of modes in a system involved in turbulence is high enough to qualitatively simulate most of processes but significantly smaller then threshold which gives us quantitative agreement with statistical description, like kinetic equation. Such regime takes place in numerical simulation, essentially finite systems etc.

## On the transition from regular to irregular motion as travel on a Riemann surface

2 September 2005 in 11:30

P.M. Santini

We introduce a simple Hamiltonian 3-body problem in the plane providing the prototype of a mechanism explaining the transition from regular to irregular motion as travel on Riemann surfaces.

## Quasi-planar steep water waves

6 May 2005 in 11:30

V.P. Ruban

A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not a surface slope, but it is the ratio of a typical wave length to a large transversal scale along the second horizontal coordinate. A first-order correction for the Hamiltonian functional is calculated, and the corresponding equations of motion are derived for steep water waves over an arbitrary non-uniform quasi-1D bottom profile.

## Wave Function Collapse in a Mesoscopic Device

25 February 2005 in 11:30

G.B. Lesovik, A.V. Lebedev, and G. Blatter

We determine the non-local in time and space current-current cross correlator〈(x1, t1)(x2, t2)〉in a mesoscopic conductor with a scattering center at the origin. Its excess part appearing at finite voltage exhibits a unique dependence on the retarded variable t1t2 – (| x1| – | x2|)/vF, with vF the Fermi velocity. The non-monotonic dependence of the retardation on x1 and its absence at the symmetric position x1 = – x2 is a signature of the wave function collapse, which thus becomes amenable to observation in a mesoscopic solid state device.

## Decay of Richtmyer-Meshkov turbulence

14 January 2005 in 11:30

N.A. Inogamov, A.M. Oparin

Impulsive acceleration g(t) propto delta(t) imposed on randomly perturbed plane surface produces random velocity field near the surface. The surface separates two incompressible ideal (Re=infinity) fluids with different densities. Random velocity field moves contact surface and so mixes fluids. We consider how velocity field gradually decay in time.

## Emission of matter from condensed targets after heating by ultrasoft laser pulse

3 December 2004 in 11:30

S.I. Anisimov, N.A. Inogamov, Yu.V. Petrov

Heating due to absorption of a part of energy of a laser pulse is the reason of complex motion of substance of a target including melting, spallation and spinodal decomposition. As a result inhomogeneous emission cloud and a crater are formed. We study such processes using hydrodynamical and molecular dynamics simulations.

## Water waves over a time-dependent bottom: Exact description for 2D potential flows

19 November 2004 in 11:30

V.P. Ruban

Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so called conformal variables are derived for an arbitrary time-evolving bottom parameterized by an analytical function. An efficient numerical method for the obtained equations is suggested.

## Fully frustrated XY-model on a dice lattice

12 November 2004 in 11:30

S.E. Korshunov

Note: The previous talk was about 1/3 of flux quantum per plaquette.

## A neutron time focus lens

17 September 2004 in 11:30

R. Gaeler, P. Grigoriev, E.I. Kats

We examine in an analytic way imaging effects of temporal neutron lenses created by traveling non-homogeneous magnetic fields. It is shown how more neutrons of an available neutron flux can be compressed into a desired momentum, space, or time interval. To illustrate the issue we present a special solution (constant acceleration for each neutron during the full time of magnetic lens action) providing theoretically an arbitrary good time resolution. From the physical and technological aspect, no basic restrictions for a realization of such a system exist.
Applications may concern neutron instruments, where temporal imaging can enhance intensity and/or time resolution. New fields of application for high resolution neutron time of flight spectrometry can be opened.

## Water waves over a strongly inhomogeneous bottom

10 September 2004 in 11:30

V.P. Ruban

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the variational method for arbitrary seabed shape parameterized by an analytical function. As applications of this theory, band structure of linear waves over periodic bottoms is calculated, and evolution of a strong solitary wave running from a deep region to a shallow region is numerically simulated, as well as transformation of a solitary wave over an underwater barrier.

## Tunable Fermi-Edge Resonance and Non-Commuting Scattering Matrices

21 May 2004 in 11:30

D. Abanin, L.S. Levitov

Resonant tunneling into an open quantum dot is proposed as a vehicle to achieve a tunable Fermi-edge resonance of a Mahan-Nozieres-deDominicis form with a variable exponent in the I-V characteristic. The effect of scattering in a mesoscopic quantum dot on the exponent is shown to depend on a single parameter, the reflection amplitude of an extended scattering matrix of the system. Changing the reflection coefficient by varying the dot coupling to the leads and scattering inside the dot allows to explore a wide range of exponents.

## Topological percolation on a square lattice

27 February 2004 in 11:30

O.A. Vasilyev, S.K. Nechaev

We investigate the "topological percolation", i.e. the formation of an infinite cluster of mutually entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the topological percolation threshold and demonstrate that the critical exponents of topological phase transition coincide with the ones of the standard 2D bond percolation. Our numerical check confirms well obtained analytical results.

## Charge transport through a SET with a mechanically oscillating island

30 January 2004 in 11:30

N.M. Chtchelkatchev, W. Belzig, and C. Bruder

We consider a single-electron transistor (SET) whose central island is a nanomechanical oscillator. The gate capacitance of the SET depends on the mechanical displacement, thus, the vibrations of the island vibrations may strongly influence the current-voltage characteristics, current noise, and higher cumulants of the current. Harmonic oscillations of the island and oscillations with random amplitude (e.g., due to the thermal activation) change the transport characteristics in a different way. The noise spectrum has a peak at the frequency of the island oscillations; when the island oscillates harmonically, the peak reduces to a δ-peak. We show that knowledge of the SET transport properties helps to determine in what way the island oscillates, to estimate the amplitude, and the frequency of the oscillations.

## Forwarding stimulated Brillouin scattering instability of a spatially and temporally incoherent laser beam

17 October 2003 in 11:30

P.M. Lushnikov

Spatial and temporal incoherence of laser beam is used to suppress self-focusing in experiments on inertial confinement fusion. It is found a temporal instability due to forward stimulated Brillouin scattering, which couples the beam to transversely propagating low frequency ion acoustic waves. Instability can result in strong self-focusing even for very short beam correlation time. Outside the instability region, the wave kinetic equation is derived which describes stationary diffusion of laser beam.

## On (1+1)D anisotropic ballistic deposition with links to the Ulam problem and (2+1)D directed percolation

26 September 2003 in 11:30

S.K. Nechaev

Incompressible, inviscid, irrotational, and unsteady flows with circulation Γ around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a two-dimensional (2D) cavity with a constant area A, exact pseudo-differential equations of motion are derived, based on variables that determine a conformal mapping of the unit circle exterior into the region occupied by the fluid. A closed expression for the Hamiltonian of the 2D system in terms of canonical variables is obtained. Stability of a stationary drifting 2D hollow vortex is demonstrated, when the circulation is relatively large, gA3/22<< 1. For a circulation-dominated regime of three-dimensional flows a simplified Lagrangian is suggested, inasmuch as the bubble shape is well described by the center-line g{R}(ξ,t) and by an approximately circular cross-section with relatively small area, A(ξ,t)<< (oint |g{R}'|dξ)2 In particular, a finite-dimensional dynamical system is derived and approximately solved for a vertically moving axisymmetric vortex ring bubble with a compressed gas inside.

## Toroidal bubbles with circulation in ideal hydrodynamics. A variational approach

19 September 2003 in 11:30

V.P. Ruban, J.J. Rasmussen

Incompressible, inviscid, irrotational, and unsteady flows with circulation Γ around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a two-dimensional (2D) cavity with a constant area A, exact pseudo-differential equations of motion are derived, based on variables that determine a conformal mapping of the unit circle exterior into the region occupied by the fluid. A closed expression for the Hamiltonian of the 2D system in terms of canonical variables is obtained. Stability of a stationary drifting 2D hollow vortex is demonstrated, when the circulation is relatively large, gA3/22 ≪ 1. For a circulation-dominated regime of three-dimensional flows a simplified Lagrangian is suggested, inasmuch as the bubble shape is well described by the center-line g{R}(ξ,t) and by an approximately circular cross-section with relatively small area, A(ξ,t) ≪ (∮ |g{R}'|dξ)2 In particular, a finite-dimensional dynamical system is derived and approximately solved for a vertically moving axisymmetric vortex ring bubble with a compressed gas inside.

## Decoherence due to nodal quasiparticles in D-wave qubits

25 April 2003 in 11:30

Ya.V. Fominov, A.A. Golubov, M.Yu. Kupriyanov

We study the Josephson junction between two d-wave superconductors, which is discussed as an implementation of a qubit. We propose an approach that allows to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.

## Triplet proximity effect in FSF trilayers

18 April 2003 in 11:30

Ya.V. Fominov, A.A. Golubov, M.Yu. Kupriyanov

We study the critical temperature Tc of FSF trilayers (F is a ferromagnet, S is a singlet superconductor), where the triplet superconducting component is generated at noncollinear magnetizations of the F layers. An exact numerical method is employed to calculate Tc as a function of the trilayer parameters, in particular, mutual orientation of magnetizations. Analytically, we consider limiting cases. Our results determine conditions which are necessary for existence of recently investigated odd triplet superconductivity in SF multilayers.

## Phase diagram of a surface superconductor in parallel magnetic field

18 April 2003 in 11:30

O.V. Dimitrova

Detailed theory of phase diagram of clean 2D surface superconductor in a parallel magnetic field is presented. Regular spin-orbital interaction of the Rashba type leads to the inhomogeneous superconductive state of the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) type. We consider the case of relatively strong Rashba interaction and show that at low temperatures the LOFF-type state is separated from the usual homogeneous state by the first-order phase transition line. At higher temperatures new "helical" state intervenes between uniform BCS state and LOFF-like state. At the second-order transition line between BCS state and helical state one component of the superfluid density vanishes.

## On the Aizenman exponent in critical percolation

21 March 2003 in 11:30

L.N. Shchur, T. Rostunov

The probabilities of clusters spanning a hypercube of dimensions two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen--Kopelman algorithm combined with Grassberger's "go with the winner" strategy for the site percolation. We carried out a finite-size analysis of the data and found that the probabilities confirm Aizenman's proposal of the multiplicity exponent for dimensions three to five. A crossover to the mean-field behavior around the upper critical dimension is also discussed.

## New problems in perturbation theory and their solutions for generic case

22 November 2002 in 11:30

S.V. Savchenko

All the people are used to thinking that only new eigenvalues which appear in a small neighborhood of a fixed eigenvalue λ of the original operator A are considered in the classical perturbation theory. However, if the number of linear independent eigenvectors for λ is greater than the rank r of a perturbation B, then λ must also be in the spectrum of the new operator C = A + B. What can one say about the change of the spectral properties of λ when the matrix A is replaced by C? In our paper we show that a generic perturbation of rank r changes the Jordan form of λ in the following way: r largest Jordan blocks disappear and all the others remain the same. For the new matrix, the part of a Jordan basis corresponding to the eigenvalue is constructed. By means of the resolvent technique and the Binet-Cauchy formula we obtain the equation of the critical surface in the space of matrix entries of a perturbation out which the typical change of the spectral properties takes place. For the new eigenvalues we develop the first order perturbation theory.

## Local approximation for contour dynamics in effectively two-dimensional ideal electron-magnetohydrodynamic flows

27 September 2002 in 11:30

V.P. Ruban and S.L. Senchenko

The evolution of piecewise constant distributions of a conserved quantity related to the frozen-in canonical vorticity in effectively two-dimensional incompressible ideal EMHD flows is analytically investigated by the Hamiltonian method. The study includes the case of axisymmetric flows with zero azimuthal velocity component and also the case of flows with the helical symmetry of vortex lines. For sufficiently large size of such a patch of the conserved quantity, a local approximation in the dynamics of the patch boundary is suggested, based on the possibility to represent the total energy as the sum of area and boundary terms. Only the boundary energy produces deformation of the shape with time. Stationary moving configurations are described.

## Disclination motion in liquid crystalline films

7 June 2002 in 11:30

E.I. Kats, V.V. Lebedev, S.V. Malinin

We present theoretical study of a single disclination motion in a thin free standing liquid crystalline film. Back-flow effects and own dynamics of the orientational degree of freedom (bond or director angle) are included. We find the the orientation field and the hydrodynamic velocity distribution around the moving disclination, what allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.

## Interlayer magnetotransport in quasi-2D metals

31 May 2002 in 11:30

P.D. Grigoriev

The Shubnikov-de Haas effect in quasi-two-dimensional normal metals is studied. The interlayer conductivity is calculated using the Kubo formula. The electron scattering on short-range is considered in the self-consistent Born approximation. The result obtained differs from that derived from the Boltzmann transport equation. This difference is shown to be a general feature of conductivity in magnetic field. A detailed description of the two new qualitative effects — the field-dependent phase shift of beats and of the slow oscillations of conductivity is provided. The results obtained are applicable to strongly anisotropic organic metals and to other quasi-two-dimensional compounds.

## Nonsinusoidal current-phase relation in SFS Josephson junctions

31 May 2002 in 11:30

Ya.V. Fominov, A.A. Golubov, M.Yu. Kupriyanov

Various types of the current-phase relation I(φ) in superconductor-ferromagnet-superconductor (SFS) point contacts and planar double-barrier junctions are studied in the limit of thin diffusive ferromagnetic interlayers. The physical mechanisms leading to highly nontrivial I(φ) dependence are identified by studying the spectral supercurrent density. These mechanisms are also responsible for the 0-π transition in SFS Josephson junctions.

## Universality of the crossing probability for the Potts model for q = 1, 2, 3, 4

27 April 2002 in 11:30

O.A. Vasiliev

The universality of the crossing probability πhs of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the q-state Potts model for q = 2, 3, 4 and for the percolation q = 1. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction πhs has universal form πhs = A(q) Q(z) for q =1, 2, 3, 4 as a function of the scaling variable z = [b(q)L1/ν(q)(ppc(q,L)) ]ζ(q). Here, p = 1 − exp(−β) is the probability of a bond to be closed, A(q) is the nonuniversal crossing amplitude, b(q) is the nonuniversal metric factor, ζ(q) is the nonuniversal scaling index, ν(q) is the correlation length index. The universal function Q(x) ≃ exp(-z). Nonuniversal scaling factors was found numerically.

## Gravity or convective turbulent mixing

19 April 2002 in 11:30

N.A. Inogamov, A.M. Oparin

Rayleigh-Taylor instability (RTI) is important for inertial confinement fusion (ICF), astrophysics and for atmospheric and oceanological applications. Mechanics of RTI is similar to the mechanics of convection. Therefore it is meaningful to consider both phenomena from common positions. The first part of work is devoted to this. The role of geometrical restrictions as lateral walls or horizontal plates is analyzed in this part. The structure of near-wall layers near such plates is studied. In the second part the internal structure of zone of RT turbulence (TMZ - turbulent mixing zone) is investigated numerically in case of mixing near a separation surface of two liquids of different density.
(i) Existence of fast descending and ascending jets is revealed. Speed of movement of substance in them exceed speed of TMZ front. Deceleration of the fast moving jets occurs in a small vicinity of front. Such sharp deceleration results in occurrence of spots in which absolute values of deceleration are high. They exceed archimedean value gA = (1-μ) g and are much larger than mean acceleration ddot h+ of front, where μ=ρl/ρh <1 - is the ratio of densities. Spot is formed in a place of crossing of front and a jet. Other interesting detail of a mixing zone is occurrence of small areas of sharp pressure drop. In them there is a strong acceleration of a light liquid.
(ii) The questions on characteristic horizontal scale of structures from bubbles and jets in a TMZ and on a spectrum of long-wave fluctuations are investigated.

## Neravnovesnye effekty pri tunnelirovanii cherez vzaimodeistvuyushchie andersonovskie primesi

22 March 2002 in 11:30

N. Maslova (MGU-FIAN)

Доклад по докторской диссертации.

## Random diffusion of optical pulse width in a disordered anisotropic optical media

18 January 2002 in 11:30

P.M. Lushnikov

A propagation of optical pulse in a one-dimensional optical media (optical fiber) with anisotropy disorder and random dispersion is described by a vector nonlinear Schrödinger equation with random coefficients. An averaged pulse width is shown to diffuse with propagation distance along optical fiber.

## Reservoir as a source for probability in quantum mechanics

14 December 2001 in 11:30

G.B. Lesovik

We propose a concept of theory of measurement in quantum mechanics. The result of the measurement in our concept is determined by the state of all involoved reservoirs (including the detector). Thus the reservoirs variables serve as a non-local "hidden" variables. We discuss the problems of derivation of the "psi squared" (due to Born) rule from the first principles. We discuss how one can technically to demonstrate the wave packet reduction, key question in the problem of measurement. We propose a way to resolve the "Schrödinger cat" paradox. Finally we discuss a connection of flicker and shot noise with the interpretation of quantum mechanics we proposed.

## Upper critical field in a trigonal unconventional superconductor (UPt3)

7 December 2001 in 11:30

P.L. Krotkov, V.P. Mineev

A theory of the upper critical field in a trigonal superconductor with a two-component order-parameter is developed. We demonstrate the existence of sixfold modulations of the upper critical field in the basal plane. The form of the angular dependence of Hc2 in the plane of the main symmetry axis is studied in the whole range of phenomenological rigidity coefficients. A qualitative dependence Hc2 in the heavy fermion superconductor UPt3 that has been recently found to possess trigonal crystalline structure.

## Spin susceptibility of the superfluid 3He-B in aerogel

30 November 2001 in 11:30

V.P. Mineev and P.L. Krotkov

The temperature dependence of paramagnetic susceptibility of the superfluid He-B in aerogel is found. Calculations have been performed for an arbitrary phase shift of s-wave scattering in the framework of BCS weak coupling theory and the simplest model of aerogel as an aggregate of homogeneously distributed ordinary impurities. Both limiting cases of the Born and unitary scattering can be easily obtained from the general result. The existence of gapless superfluidity starting at the critical impurity concentration depending on the value of the scattering phase has been demonstrated. While larger than in the bulk liquid the calculated susceptibility of the B-phase in aerogel proves to be conspicuously smaller than that determined experimentally in the high pressure region.

## Schwinger type processes via branes and their gravity duals

12 October 2001 in 11:30

A. Gorsky, K. Saraikin and K. Selivanov

We consider Schwinger type processes involving the creation of the charge and monopole pairs in the external fields and propose interpretation of this processes via corresponding brane configurations in Type IIB string theory. We propose simple description of some interesting processes like monopole/dyon transitions in the electric field and W-boson/monopole transition in the magnetic field using the brane language. We study nonperturbative pair production in the strong coupling regime using the AdS/CFT correspondence. The treatment of the similar processes in the noncommutative theories where noncommutativity is traded for the background fields is presented and the possible role of the critical magnetic field which is S-dual to the critical electric field is discussed.

## New algebraic structures related with Baxter Q-operator

28 September 2001 in 11:30

A. Belavin, A. Odesskii, R. Usmanov

Mi rassmatrivaem neprivodimie ciklicheskie predstavleniya algebri matric monodromii, sootvetstvuyushie R-matrice shestivershinnoi modeli. V kornyah iz edinici Q-operator Baxtera mojet bit predstavlen kak sled proizvedeniya L-operatorov, otvechayushih odnomu iz takih predstavlenii. Dlya nego spravedlivo TQ-uravnenie.