Scarring in Rough Rectangular Billiards.

We study the mechanism of scarring of eigenstates in rectangular billiards with slightly corrugated surfaces and show that it is very different from that known in Sinai and Bunimovich billiards. We demonstrate that there are two sets of scar states. One set is related to the bouncing ball trajectories in the configuration space of the corresponding classical billiard.

Spectrum statistics in the integrable Lieb-Liniger model.

We address the old and widely debated question of the spectrum statistics of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of one-dimensional interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is to reveal the characteristic properties of energy levels in dependence of the model parameters. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum.

Timescales in the quench dynamics of many-body quantum systems: Participation ratio versus out-of-time ordered correlator.

We study quench dynamics in the many-body Hilbert space using two isolated systems with a finite number of interacting particles: a paradigmatic model of randomly interacting bosons and a dynamical (clean) model of interacting spins-1/2. For both systems in the region of strong quantum chaos, the number of components of the evolving wave function, defined through the number of principal components N_{pc} (or participation ratio), was recently found to increase exponentially fast in time [Phys. Rev.

Emergence of correlations in the process of thermalization of interacting bosons.

We address the question of the relevance of thermalization and scrambling to the increase of correlations in the quench dynamics of an isolated system with a finite number of interacting bosons. Specifically, we study how, in the process of thermalization, the correlations between occupation numbers increase in time, resulting in the emergence of the Bose-Einstein distribution. Despite the exponential increase of the number of principal components of the wave function, we show, both analytically and numerically, that the two-point correlation function before saturation increases quadratically in time according to perturbation theory.

Exponentially fast dynamics of chaotic many-body systems.

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width Γ of the local density of states and is associated with the Kolmogorov-Sinai entropy for systems with a well-defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell.