E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach
Theory of the quantal level statistics of classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV)\cite{MT03,MMT09}, is successfully extended to the study of \(E(K,L)\) function...
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Published in | arXiv.org |
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Main Author | |
Format | Paper Journal Article |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
21.08.2022
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Subjects | |
Online Access | Get full text |
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Summary: | Theory of the quantal level statistics of classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV)\cite{MT03,MMT09}, is successfully extended to the study of \(E(K,L)\) function which constitutes a fundamental measure to determine most statistical observables of quantal levels in addition to LSD and LNV. In the theory of Makino et al., the eigenenergy level is regarded as a superposition of infinitely many components whose formation is supported by the Berry-Robnik approach in the far semiclassical limit\cite{Robn1998}. We derive the limiting \(E(K,L)\) function in the limit of infinitely many components and elucidates its properties when energy levels show deviations from the Poisson statistics. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2208.09845 |