Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise

TL;DR

This paper introduces a method to estimate the ergodization time in chaotic many-particle systems using equilibrium noise and time reversal, validated through numerical simulations of coupled Bose-Einstein condensates.

Contribution

The paper presents a novel approach to measure ergodization time via equilibrium noise and time reversal, linking classical chaos indicators with quantum correlators.

Findings

Method accurately estimates ergodization time in simulations.

Validates the approach with Bose-Einstein condensate models.

Connects classical chaos metrics with quantum out-of-time-order correlators.

Abstract

We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics (Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system's dynamics. We validate the method by numerical simulation of an array of coupled Bose-Einstein condensates in the regime describable by the discrete Gross-Pitaevskii equation. The quantity of interest for the method is a counterpart of out-of-time-order correlators (OTOCs) in the quantum regime.