Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-09-15
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.
Prosen Tomaz
Seligman Thomas H.
Weidenmueller Hans A.
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