# Seminars

Regular seminars are held on Thursdays in the Kapitza Institute in Moscow and on Fridays at the scientific council of the Landau Institute in Chernogolovka.

Departments of the institute hold their own seminars; the topic are determined by the scientific orientation of the related department.

Seminars information is also sent via e-mail. If you want to receive seminar announcements, please subscribe.

## Limit shape phase transitions. A merger of Arctic circles

29 October, the day after tomorrow in 15:30 at scientific council

Alexander Abanov (SUNY Stony Brook)

A limit shape phenomenon in statistical mechanics is the appearance of a most probable macroscopic state. This state is usually characterized by a well-defined boundary separating frozen and liquid spatial regions. The earliest studies related to this phenomenon in the context of crystal shapes are in works by Pokrovsky and Talapov [1]. We will review a few examples of the models leading to the appearance of limit shapes. Then we consider a class of topological phase transitions in the limit shape problem of statistical mechanics. The problem considered is generally known as the Arctic circle problem. The considered transition can be visualized as the merging of two melted regions (Arctic circles). We establish the mapping, which identifies the transition as the transition known in lattice QCD and random matrix problems [2,3]. The transition is a continuous phase transition of the third order. We identify universal features of the limiting shape close to the transition using the hydrodynamic description.

[1] V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979). "Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals."

[2] D. J. Gross and E. Witten, Phys. Rev. D, 21 (2): 446, (1980). "Possible third-order phase transition in the large-n lattice gauge theory"; S. R. Wadia, Phys. Lett. B 93, 403 (1980). "$N=\infty$ phase transition in a class of exactly soluble model lattice gauge theories."

[3] M. R. Douglas and V. A. Kazakov. Phys. Lett. B, 319 (1-3): 219–230, 1993. "Large n phase transition in continuum QCD2."

[1] V. L. Pokrovsky and A. L. Talapov, Phys. Rev. Lett. 42, 65 (1979). "Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals."

[2] D. J. Gross and E. Witten, Phys. Rev. D, 21 (2): 446, (1980). "Possible third-order phase transition in the large-n lattice gauge theory"; S. R. Wadia, Phys. Lett. B 93, 403 (1980). "$N=\infty$ phase transition in a class of exactly soluble model lattice gauge theories."

[3] M. R. Douglas and V. A. Kazakov. Phys. Lett. B, 319 (1-3): 219–230, 1993. "Large n phase transition in continuum QCD2."

## Many-body delocalisation as symmetry breaking

12 November in 11:30 at scientific council

John Chalker (Physics Department, University of Oxford)

I will start this talk with an overview of recent work on quantum dynamics in many body systems far from equilibrium. This work has led to an understanding from the
perspective of quantum information, of how a such systems may approach an
equilibrium state at long times, in which initial conditions are effectively forgotten. It
has also led to an appreciation that there are classes of system in which an
equilibrium state is not reached at long times. One of these classes is made up of
many-body localised systems, in which randomness in the Hamiltonian is
responsible for a long-lived memory of the initial state of a system. By varying the
strength of randomness, a transition can be induced between localised and ergodic
phases, which seems very different from conventional symmetry-breaking phase
transitions.

In the second part of the talk I will discuss minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will examine the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models.

Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) and Phys. Rev. Lett. 127, 026802 (2021)

In the second part of the talk I will discuss minimal models for quantum chaos and many-body localisation. The models are Floquet quantum circuits for lattice spin systems, in which time evolution is generated by unitary gates that couple neighbouring sites. In particular, I will examine the circumstances in which a version of the so-called diagonal approximation (originally developed for the semiclassical limit in low-dimensional chaotic systems) can be applied to these systems. Within this framework I will show that the many-body delocalisation transition can be seen as a form of symmetry breaking transition, having many of the features generally associated with conventional phase transitions in classical statistical mechanical models.

Joint work with Sam Garratt: Phys. Rev. X 11, 021051 (2021) and Phys. Rev. Lett. 127, 026802 (2021)

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

19 November in 11:30 at scientific council

__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.

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 in 11:30 at scientific council (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 in 11:30 at scientific council (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.