Quantum statistical mechanics in a closed system

J. M. Deutsch
Phys. Rev. A 43, 2046 – Published 1 February 1991
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Abstract

A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution. For systems where the different degrees of freedom are uncoupled, situations are discussed that show a violation of the usual statistical-mechanical rules. By adding a finite but very small perturbation in the form of a random matrix, it is shown that the results of quantum statistical mechanics are recovered. Expectation values in energy eigenstates for this perturbed system are also discussed, and deviations from the microcanonical result are shown to become exponentially small in the number of degrees of freedom.

  • Received 4 December 1989

DOI:https://doi.org/10.1103/PhysRevA.43.2046

©1991 American Physical Society

Authors & Affiliations

J. M. Deutsch

  • Department of Physics, University of California, Santa Cruz, California 95064
  • The James Franck Institute, 5640 South Ellis Avenue, Chicago, Illinois 60637

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Issue

Vol. 43, Iss. 4 — February 1991

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