Volume 55, Number 1, July 2001
|Page(s)||12 - 18|
|Published online||01 December 2003|
Random matrix ensembles for semi-separable systems
Physics Department, Faculty of Mathematics and Physics
University of Ljubljana - Slovenia
2 Centro de Ciencias Fisicas, UNAM, Cuernavaca and Centro Internacional de Ciencias - Cuernavaca, Mexico
3 Max Planck Institut für Kernphysik - Heidelberg, Germany
Accepted: 9 April 2001
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 ) 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.
PACS: 05.45.Mt – Semiclassical chaos ("quantum chaos" ) / 03.65.Fd – Algebraic methods
© EDP Sciences, 2001
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