General relaxation time of the fidelity for isolated quantum thermodynamic systems

Abstract

General evaluation of the relaxation time to equilibrium is usually considered as difficult, since it would strongly depend on the model of interest. In this paper, we provide a generic initial relaxation time of the fidelity for the isolated large systems. The decay of the fidelity is a combination of the Lorentzian and a sinusoidal oscillation. We calculate the relaxation time of the Lorentzian envelop, and the period of the oscillation. Remarkably, these two time scales are the same order when the energy range of the microcanonical state is larger than the thermal fluctuation. Also, the power law decay generally exists for long time regime.

arXiv comment4 pages, to appear in Journal of the Physical Society of Japan

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• Transportless equilibration in isolated many-body quantum systems
• Relative purity, speed of fluctuations, and bounds on equilibration times
• Relaxation to Gaussian Generalized Gibbs Ensembles in Quadratic Bosonic Systems in the Thermodynamic Limit
• Typical Pure Nonequilibrium Steady States
• The approach to equilibrium in a macroscopic quantum system for a typical nonequilibrium subspace
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• Quasi adiabatic dynamics of energy eigenstates for solvable quantum system at finite temperature