Estimate of equilibration times of quantum correlation functions in the thermodynamic limit based on Lanczos coefficients

TL;DR

This paper proposes a method to estimate the equilibration times of local observables in quantum chaotic systems using Lanczos coefficients, suggesting equilibration occurs rapidly in the thermodynamic limit.

Contribution

The authors introduce a scheme based on the recursion method to estimate equilibration times from Lanczos coefficients in large quantum systems.

Findings

Finite Lanczos coefficients can accurately estimate equilibration times.

Equilibration occurs on timescales much shorter than the age of the universe.

Analytical support confirms numerical results.

Abstract

We study the equilibration times $T_\text{eq}$ of local observables in quantum chaotic systems by considering their auto-correlation functions. Based on the recursion method, we suggest a scheme to estimate $T_\text{eq}$ from the corresponding Lanczos coefficients that is expected to hold in the thermodynamic limit. We numerically find that if the observable eventually shows smoothly growing Lanczos coefficients, a finite number of the former is sufficient for a reasonable estimate of the equilibration time. This implies that equilibration occurs on a realistic time scale much shorter than the life of the universe. The numerical findings are further supported by analytical arguments.