Pair correlations of quantum chaotic maps from supersymmetry

Details Pair correlations of quantum chaotic maps from supersymmetry Pair correlations of quantum chaotic maps from supersymmetry

1998-12-16

arxiv.org/abs/chao-dyn/9812023v1

Physics

Condensed Matter

LaTeX2e, 28 pages, lectures given at the NATO Advanced Study Institute, Cambridge UK, September 1997; to appear in Supersymmet

Scientific paper

A conjecture due to Bohigas, Giannoni and Schmit (BGS), stating that the energy level correlations of quantum chaotic systems generically obey the laws of random matrix theory, is given a precise formulation for quantized symplectic maps. No statement is made about any individual quantum map. Rather, a few-parameter ensemble of maps is considered, such that the deterministic map is composed with a diffusion operator on average. The ensemble is a ``quantum'' one, which is to say that the diffusion operator contracts to the identity in the classical limit. It is argued that the BGS conjecture is true on average over such an ensemble, provided that the classical map is mixing. The method used is closely related to the supersymmetric formalism of Andreev et al for chaotic Hamiltonian systems.

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