We study the equilibration times $T_{\mathrm{eq}}$ of local observables in quantum chaotic systems by considering their autocorrelation functions. Based on the recursion method, we suggest a scheme to estimate $T_{\mathrm{eq}}$ 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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• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics
• Quantum statistical mechanics
• Quantum thermodynamics
• 1-dimensional spin chains
• Many-body techniques
• Spin lattice models