Random-Matrix Ensembles for Semi-Separable Systems

Abstract

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.

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

References in corpus (3)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Composed ensembles of random unitary matrices
• Multichannel Quantum Defect Theory: a Quantum Poincare Map

Cited by in corpus (6)

• Non-universal level statistics in a chaotic quantum spin chain
• Decoherence of an $n$-qubit quantum memory
• Integrals of monomials over the orthogonal group
• Unified theory of bound and scattering molecular Rydberg states as quantum maps
• Integration over matrix spaces with unique invariant measures
• One, Two, and $n$ Qubit Decoherence