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Journal of the Physical Society of Japan

Generic Evaluation of Relaxation Time for Quantum Many-Body Systems: Analysis of the System Size Dependence

Takaaki Monnai

Published Apr 15, 2013• 17 citations
Publisher

Abstract

General evaluation of the relaxation time to equilibrium remains as a subtle unsolved problem, partially because of its possible dependence on the specific features of models. We evaluate the relaxation time of expectation values for generic isolated quantum many-body systems, and especially show that it at most polynomially depends on the system size. This provides a first model-independent quantitative analysis of the relaxation time. The estimation holds when the Hamiltonian is non-integrable, the initial deviation of the quantity of interest is order of its spectral norm defined on a finite space, and the relaxation process is essentially monotonic.

DOI
10.7566/jpsj.82.044006

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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.
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