Equilibration time in many-body quantum systems

TL;DR

This paper investigates the timescale for equilibration in disordered many-body quantum systems, revealing exponential scaling with system size when spectral correlations are considered, and power-law scaling otherwise.

Contribution

It provides a detailed numerical analysis of equilibration times, highlighting the importance of spectral correlations in determining scaling behavior.

Findings

Equilibration time scales exponentially with system size when spectral correlations are included.

Neglecting spectral correlations leads to a power-law scaling with a larger exponent.

Spectral correlations significantly influence the dynamics of quantum thermalization.

Abstract

Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from perturbation to equilibration, of a paradigmatic disordered many-body quantum system in the chaotic regime. We investigate how the equilibration time depends on the system size and observables. We show that if dynamical manifestations of spectral correlations in the form of the correlation hole ("ramp") are taken into account, the time for equilibration scales exponentially with system size, while if they are neglected, the scaling is better described by a power law with system size, though with an exponent larger than what is expected for diffusive transport.