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

• URL: http://arxiv.org/abs/2412.15932v2
• Date: Thu, 03 Jul 2025 06:35:19 GMT
• Title: Estimate of equilibration times of quantum correlation functions in the thermodynamic limit based on Lanczos coefficients
• Authors: Jiaozi Wang, Merlin Füllgraf, Jochen Gemmer,
• Abstract summary: We study the equilibration times $T_texteq$ of local observables in quantum chaotic systems.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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