QUANTUM CHAOS, IRREVERSIBLE CLASSICAL DYNAMICS, AND RANDOM-MATRIX THEORY

The Bohigas-Giannoni-Schmit conjecture stating that the statistical sp ectral properties of systems which are chaotic in their classical limi t coincide with random matrix theory (RMT) is proved. A new semiclassi cal field theory for individual chaotic systems is constructed in the framework of a nonlinear sigma model. The low lying modes are shown to be associated with the Perron-Frobenius (PF) spectrum of the underlyi ng irreversible classical dynamics. It is shown that the existence of a gap in the PF spectrum results in RMT behavior. Moreover, our formal ism offers a way of calculating system specific corrections beyond RMT .