Quantum chaos, irreversible classical dynamics, and random matrix theory

A. V. Andreev, O. Agam, B. D. Simons, B. L. Altshuler

Research output: Contribution to journalArticlepeer-review

164 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3947-3950
Number of pages4
JournalPhysical Review Letters
Volume76
Issue number21
DOIs
Publication statusPublished - 20 May 1996
Externally publishedYes

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