Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory
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.
- Publication:
-
Physical Review Letters
- Pub Date:
- May 1996
- DOI:
- 10.1103/PhysRevLett.76.3947
- arXiv:
- arXiv:cond-mat/9601001
- Bibcode:
- 1996PhRvL..76.3947A
- Keywords:
-
- Condensed Matter
- E-Print:
- 4 pages, revtex, no figures