# In Print

## Dual description of integrable sigma-models

11 January 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.

The report is based joint work with Fateev and Spodyneiko.

## Deautonomization of cluster integrable systems

11 January 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.

## Elektronnye svoistva neuporyadochenogo grafena

28 December 2018 in 11:30

Pavel Ostrovskii

Doklad po predstavlyaemoi k zashchite doktorskoi dissertatsii.

## 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)

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)

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)

V.E. Adler, A.B. Shabat

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.,

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).

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

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.

## Poverkhnostnyi impedans na diffuznoi granitse kiral’nogo p-volnovogo sverkhprovodnika

16 November 2018 in 11:30

Ya.V. Fominov

Vychislena lokal’naya kompleksnaya provodimost’ i obuslovlennyi eyu poverkhnostnyi impedans na diffuznoi granitse kiral’nogo p-volnovogo sverkhprovodnika. Imenno kiral’noe p-volnovoe sostoyanie schitaetsya naibolee veroyatnym v sverkhprovodyashchem rutenate strontsiya Sr

Doklad osnovan na rabote S. V. Bakurskiy, Ya. V. Fominov, A. F. Shevchun, Y. Asano, Y. Tanaka, M. Yu. Kupriyanov, A. A. Golubov, M. R. Trunin, H. Kashiwaya, S. Kashiwaya, and Y. Maeno, "Local impedance on a rough surface of a chiral p-wave superconductor", Phys. Rev. B 98, 134508 (2018); https://arxiv.org/pdf/1807.11735.pdf

_{2}RuO_{4}. Ono anizotropnoe i pri etom polnost’yu shchelevoe (modul’ parametra poryadka fiksirovan, a faza zavisit ot napravleniya). My rassmatrivaem otklik na vneshnee elektromagnitnoe pole kak na podshchelevykh, tak i na nadshchelevykh chastotakh. Izucheny anomal’nye osobennosti poverkhnostnogo impedansa, svyazannye s generatsiei vblizi granitsy nechyotnykh po chastote sverkhprovodyashchikh korrelyatsii (sostoyanie tipa sverkhprovodimosti Berezinskogo). Teoreticheskie rezul’taty sopostavleny s izmereniyami poverkhnostnogo impedansa Sr_{2}RuO_{4}, provedyonnymi v IFTT. Nablyudaetsya kachestvennoe soglasie teorii i eksperimenta.Doklad osnovan na rabote S. V. Bakurskiy, Ya. V. Fominov, A. F. Shevchun, Y. Asano, Y. Tanaka, M. Yu. Kupriyanov, A. A. Golubov, M. R. Trunin, H. Kashiwaya, S. Kashiwaya, and Y. Maeno, "Local impedance on a rough surface of a chiral p-wave superconductor", Phys. Rev. B 98, 134508 (2018); https://arxiv.org/pdf/1807.11735.pdf

## Sverkhprovodyashchii spinovyi klapan v sistemakh so splavom Geislera

16 November 2018 in 11:30 (short)

Ya.V. Fominov

Provedeno teoreticheskoe soprovozhdenie eksperimentov po izmereniyu effekta sverkhprovodyashchego spinovogo klapana v sisteme tipa FFS (gde F — ferromagnetik, S — sverkhprovodnik). Effekt sostoit v tom, chto kriticheskaya temperatura

Doklad osnovan na sleduyushchikh rabotakh:

[1] A. Kamashev, A. Validov, N. Garif’yanov, Ya. Fominov, P. Leksin, J. Schumann, J. Thomas, V. Kataev, B. Büchner, I. Garifullin, "Isolation of proximity-induced triplet pairing channel in a superconductor/ferromagnet spin valve", EPJ Web of Conferences 185, 08001 (2018).

[2] A.A. Kamashev, A.A. Validov, J. Schumann, V. Kataev, B. Büchner, Ya.V. Fominov, I.A. Garifullin, "Increasing the performance of a superconducting spin valve using a Heusler alloy", Beilstein J. Nanotechnol. 9, 1764 (2018).

*T*sistemy zavisit ot vzaimnoi orientatsii namagnichennostei dvukh ferromagnetikov. V eksperimente v kachestve srednego F sloya byl vzyat splav Geislera Co_{c}_{2}Cr_{1-x}Fe_{x}Al, i eto pozvolilo usilit’ effekt (raznost’*T*pri parallel’noi i antiparallel’noi orientatsii) po sravneniyu s ranee issledovannymi sistemami s zhelezom. Znak effekta zavisit ot tolshchiny sloya. Teoriya ob’yasnyaet poluchennye rezul’taty. Usilenie effekta okazyvaetsya svyazano s umen’shennoi velichinoi obmennogo polya v splave Geislera._{c}Doklad osnovan na sleduyushchikh rabotakh:

[1] A. Kamashev, A. Validov, N. Garif’yanov, Ya. Fominov, P. Leksin, J. Schumann, J. Thomas, V. Kataev, B. Büchner, I. Garifullin, "Isolation of proximity-induced triplet pairing channel in a superconductor/ferromagnet spin valve", EPJ Web of Conferences 185, 08001 (2018).

[2] A.A. Kamashev, A.A. Validov, J. Schumann, V. Kataev, B. Büchner, Ya.V. Fominov, I.A. Garifullin, "Increasing the performance of a superconducting spin valve using a Heusler alloy", Beilstein J. Nanotechnol. 9, 1764 (2018).

## New integrals of motion for waves on the deep water with a free surface

16 November 2018 in 11:30 (short)

A.I. Dyachenko

Khorosho izvestno, chto v priblizhenii slaboi nelineinosti dlya voln na vode (teoriya slaboi turbulentnosti), kogda uchityvayutsya tol’ko chetyrekh-volnovye vzaimodeistviya, imeetsya integral dvizheniya - polnoe "chislo voln" (volnovoe deistvie).
Volny na glubokoi vode mogut byt’ razdeleny na dve gruppy, begushchie vlevo i begushchie vpravo.
Pokazano, chto osobye svoistva koeffitsienta chetyrekh-volnovogo vzaimodeistviya privodyat k sokhraneniyu ne tol’ko polnogo "chisla voln",
no i dvukh novykh integralov dvizheniya: "chislo voln", begushchikh vlevo, i "chislo voln", begushchikh vpravo.

## 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.

## 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.