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

166 Scopus citations


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 languageAmerican English
Pages (from-to)3947-3950
Number of pages4
JournalPhysical Review Letters
Issue number21
StatePublished - 20 May 1996
Externally publishedYes


Dive into the research topics of 'Quantum chaos, irreversible classical dynamics, and random matrix theory'. Together they form a unique fingerprint.

Cite this