Phys. Rev. Lett. 76, 3947–3950 (1996)Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix TheoryReceived 21 December 1995; published in the issue dated 20 May 1996 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. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.76.3947
DOI:
10.1103/PhysRevLett.76.3947
PACS:
05.45.+b
See AlsoComment: F. Leyvraz and T. H. Seligman, Comment on “Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory”, Phys. Rev. Lett. 79, 1778 (1997). Reply: O. Agam, A. V. Andreev, B. D. Simons, and B. L. Altshuler, Agam et al. Reply:, Phys. Rev. Lett. 79, 1779 (1997). |
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