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 L_c, 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.

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 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.

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.

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.

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).

The talk concerns the associativity equations (the WDVV system of equations), which arose in the 1990`s 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.

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.

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.

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 Nd_2−xCe_xCuO₄. This points to the presence of Néel order in this superconductor even at optimal doping.

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 p_x and p_y 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).

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.

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.

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).

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.

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.

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.

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)].

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.

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.

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.

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.