Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory

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 is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non--linear $\sigma$-model. The low lying modes are shown to be associated with the Perron--Frobenius spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

4 pages, revtex, no figures

References in corpus (3)

• Spectral Statistics Beyond Random Matrix Theory
• Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
• Spectral Statistics: From Disordered to Chaotic Systems

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