Statistical fluctuations of matrix elements in regular and chaotic systems

Y. Alhassid and M. Feingold
Phys. Rev. A 39, 374 – Published 1 January 1989
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Abstract

A combination of semiclassical arguments and random-matrix theory is used to analyze transition strengths in quantum systems whose associated classical systems are chaotic. The mean behavior is found semiclassically while the local fluctuations are characterized by a Porter-Thomas distribution. The methods are tested numerically for a system with two degrees of freedom, the coupled-rotators model. The deviations of the strength distribution from a Porter-Thomas one when the system is nonchaotic are also investigated. It is found that the distribution gets gradually wider as the classical system becomes more regular.

  • Received 1 August 1988

DOI:https://doi.org/10.1103/PhysRevA.39.374

©1989 American Physical Society

Authors & Affiliations

Y. Alhassid

  • A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06511

M. Feingold

  • The James Franck Institute, University of Chicago, Chicago, Illinois 60637

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Vol. 39, Iss. 1 — January 1989

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