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Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory | | A. V. Andreev
; O. Agam
; B. D. Simons
; B. L. Altshuler
; | | Date: |
1 Dec 1995 | | Subject: | cond-mat | | 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. | | Source: | arXiv, cond-mat/9601001 | | Other source: | [GID 875452] pmid10061153 | | Services: | Forum | Review | PDF | Favorites | |
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