Thermalization and quantum chaos in many-body interacting systems

by Prof. Fausto Borgonovi

Catholic University Brescia Italy

at Condensed Matter Seminar

Mon, 08 Mar 2021, 11:30
Zoom

Abstract

The problem of thermalization in isolated quantum many-body systems is discussed in the frame of recent experiments and old and new theoretical results. In particular, the role of quantum chaotic signatures in the process of relaxation is stressed. Starting from a very paradigmatic model of a finite number (N) of interacting particles we will demonstrate that the number of states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are chaotic and delocalized in the energy shell. The rate of the exponential growth is defined by the width $\Gamma$ of the local density of states (LDoS). In finite systems, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the thermalization and show that it is N times larger than the characteristic Heisenberg time $\hbar/\Gamma$.
Last but not least we address the question of the relevance of thermalization to the increase of correlations. 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.

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Created on 03-03-2021 by Meidan, Dganit (dganit)
Updaded on 03-03-2021 by Meidan, Dganit (dganit)