Quasiclassical Random Matrix Theory

Details Quasiclassical Random Matrix Theory Quasiclassical Random Matrix Theory

1996-05-15

arxiv.org/abs/chao-dyn/9605009v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail prange@quantum.umd.edu

Scientific paper

10.1103/PhysRevLett.77.2447

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 NxN 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.

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