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

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.

💡 Research Summary

The paper addresses the long‑standing question of why isolated quantum many‑body systems equilibrate on physically realistic time scales, far shorter than astronomical ages. The authors focus on local observables in chaotic quantum systems and define the equilibration time (T_{\text{eq}}) as the integral of the squared autocorrelation function, \