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arXiv · 0906.2051

Level statistics for nearly integrable systems

A. Y. Abul-Magd
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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.

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A. Y. Abul-Magd. 2009-06-11. Level statistics for nearly integrable systems. https://doi.org/10.1103/physreve.80.017201

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