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Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory

A. V. Andreev·O. Agam·B. D. Simons·B. L. Altshuler
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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 is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non--linear $σ$-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.

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A. V. Andreev, O. Agam, B. D. Simons, B. L. Altshuler. 1996-01-01. Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory. https://doi.org/10.1103/physrevlett.76.3947

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