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

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.

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