Localized Thermal States

It is believed that thermalization in closed systems of interacting particles can occur only when the eigenstates are fully delocalized and chaotic in the preferential (unperturbed) basis of the total Hamiltonian. Here we demonstrate that at variance with this common belief the typical situation in the systems with two-body inter-particle interaction is much more complicated and allows to treat as thermal even eigenstates that are not fully delocalized. Using a semi-analytical approach we establish the conditions for the emergence of such thermal states in a model of randomly interacting bosons. Our numerical data show an excellent correspondence with the predicted properties of {\it localized thermal eigenstates}.Comment: Proceedings of the 5th Conference on Nuclei and Mesoscopic Physics, NMP17, East Lansing (USA

Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs 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. E 99, 010101R (2019)]. Here, we ask whether the out-of-time ordered correlator (OTOC), which is nowadays widely used to quantify instability in quantum systems, can manifest analogous time-dependence. We show that $N_{pc}$ can be formally expressed as the inverse of the sum of all OTOC's for projection operators. While none of the individual projection-OTOC's shows an exponential behavior, their sum decreases exponentially fast in time. The comparison between the behavior of the OTOC with that of the $N_{pc}$ helps us better understand wave packet dynamics in the many-body Hilbert space, in close connection with the problems of thermalization and information scrambling.Comment: 11 pages, 7 figure

Transport properties of one-dimensional Kronig-Penney models with correlated disorder

Transport properties of one-dimensional Kronig-Penney models with binary correlated disorder are analyzed using an approach based on classical Hamiltonian maps. In this method, extended states correspond to bound trajectories in the phase space of a parametrically excited linear oscillator, while the on site-potential of the original model is transformed to an external force. We show that in this representation the two probe conductance takes a simple geometrical form in terms of evolution areas in phase-space. We also analyze the case of a general N-mer model.Comment: 16 pages in Latex, 12 Postscript figures include

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 $\Gamma$ of the local density of states (LDOS) 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. We estimate the time scale for the saturation and show that it is much larger than $\hbar/\Gamma$. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.Comment: 11 pages, 5 figures (as published

Generation of correlated binary sequences from white noise

This article discusses a method for generation of correlated binary sequences from white noise

Periodic and Non-Periodic Band Random Matrices: Structure of Eigenstates

The structure of eigenstates for the ensembles of standard and periodic Band Random Matrices (BRM) is analysed. The main attention is drawn to the scaling properties of the inverse participation ratio and other measures of Iocahzation Iength. Numerical data are compared with analytical results recently derived for standard BRMS of very large bond size. The data for periodic and standard BRM allow us to exhibit the influence of boundary conditions on the properties of eigenstates

Periodic and Non-Periodic Band Random Matrices: Structure of Eigenstates

The structure of eigenstates for the ensembles of standard and periodic Band Random Matrices (BRM) is analysed. The main attention is drawn to the scaling properties of the inverse participation ratio and other measures of localization length. Numerical data are compared with analytical results recently derived for standard BRMs of very large band size. The data for periodic and standard BRM allow us to exhibit the influence of boundary conditions on the properties of eigenstates