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 (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.
Original language | English |
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Pages (from-to) | 3947-3950 |
Number of pages | 4 |
Journal | Physical Review Letters |
Volume | 76 |
Issue number | 21 |
DOIs | |
State | Published - 20 May 1996 |
Externally published | Yes |