Estimate of Equilibration Times of Quantum Correlation Functions in the Thermodynamic Limit Based on Lanczos...

We study the equilibration times T_{eq} of local observables in quantum chaotic systems by considering their autocorrelation functions. Based on the recursion method, we suggest a scheme to estimate T_{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.