Quasiclassical Random Matrix Theory.

Abstract

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular, to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an $N\ifmmode\times\else\texttimes\fi{}N$ unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry (as with Dyson's circular unitary ensemble), we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.