Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory

A. V. Andreev, O. Agam, B. D. Simons, and B. L. Altshuler
Phys. Rev. Lett. 76, 3947 – Published 20 May 1996
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Abstract

The Bohigas-Giannoni-Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory (RMT) is proved. A new semiclassical field theory for individual chaotic systems is constructed in the framework of a nonlinear σ model. The low lying modes are shown to be associated with the Perron-Frobenius (PF) spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the PF spectrum results in RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

  • Received 21 December 1995

DOI:https://doi.org/10.1103/PhysRevLett.76.3947

©1996 American Physical Society

Authors & Affiliations

A. V. Andreev1,2, O. Agam1, B. D. Simons3, and B. L. Altshuler1,2

  • 1NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540
  • 2Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
  • 3Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, United Kingdom

Comments & Replies

Comment on “Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory”

F. Leyvraz and T. H. Seligman
Phys. Rev. Lett. 79, 1778 (1997)

Agam et al. Reply:

O. Agam, A. V. Andreev, B. D. Simons, and B. L. Altshuler
Phys. Rev. Lett. 79, 1779 (1997)

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Vol. 76, Iss. 21 — 20 May 1996

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