Density matrix of chaotic quantum systems

TL;DR

This paper investigates the universal properties of the density matrix in chaotic quantum systems during nonequilibrium dynamics, testing recent hypotheses through numerical simulations of spin models.

Contribution

It provides numerical validation for the proposed universal form of the density matrix elements in chaotic quantum systems.

Findings

Confirmed the universal form of density matrix elements in spin models

Demonstrated the applicability of the hypothesis across different time scales

Enhanced understanding of quantum chaos and thermalization processes

Abstract

The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal form of the observable matrix elements in the eigenbasis of Hamiltonian. It was recently proposed that the density matrix elements have also a universal form, which can be used to understand the nonequilibrium dynamics at the whole time scale, from the transient regime to the long-time steady limit. In this paper, we numerically test these assumptions for density matrix in the models of spins.