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.

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.

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.

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))

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

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.

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.

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

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

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.

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).