Level statistics for nearly integrable systems

Abstract

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble. We obtain analytical expressions for the level spacing distribution and level number variance for such a system. These expressions are successfully applied to the analysis of the resonance spectrum in a nearly integrable microwave billiard.

10 pages, 4 figures

References in corpus (8)

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• Fluctuations of the inverse participation ratio at the Anderson transition
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• New Class of Random Matrix Ensembles with Multifractal Eigenvectors
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• Unfolding of the Spectrum for Chaotic and Mixed Systems
• Entanglement in coupled kicked tops with chaotic dynamics
• On the spectral unfolding of chaotic and mixed systems
• On the similarity between Nakagami-m Fading distribution and the Gaussian ensembles of random matrix theory
• Mixing Property of Symmetrical Polygonal Billiards
• Classical and Quantum Elliptical Billiards: Mixed Phase Space and Short Correlations in Singlets and Doublets