Random-Matrix Ensembles for Semi-Separable Systems

Details Random-Matrix Ensembles for Semi-Separable Systems Random-Matrix Ensembles for Semi-Separable Systems

2000-09-15

arxiv.org/abs/nlin/0009029v2

Nonlinear Sciences

Chaotic Dynamics

7 pages with 2 eps-figures, revised version, in press at Europhysics Letters

Scientific paper

10.1209/epl/i2001-00374-9

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be diagonalized. The two eigenvector bases are related by an orthogonal (or unitary) transformation. We construct a random matrix ensemble that mimics this situation and consists of a product of a diagonal, an orthogonal, another diagonal and the transposed orthogonal matrix. The diagonal phases are chosen at random and the orthogonal matrix from Haar's measure. We derive asymptotic results (dimension N -> \infty) using Wick contractions. A new approximation for the group integration yields the next order in 1/N. We obtain a finite correction to the circular orthogonal ensemble, important in the long-range part of spectral correlations.

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