Exponentially fast dynamics of chaotic many-body systems

TL;DR

This paper shows that in isolated quantum many-body systems, the number of participating states grows exponentially after a quench, with the rate linked to the local density of states width, and confirms this with analytical and numerical results.

Contribution

It provides an analytical and numerical demonstration that the exponential growth rate of many-body states is determined by the LDOS width, connecting quantum chaos with classical entropy.

Findings

Exponential growth of participating states is confirmed analytically and numerically.

Growth rate equals the LDOS width, related to Kolmogorov-Sinai entropy.

Finite systems show saturation of exponential growth at a predictable time.

Abstract

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.