E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach

Hironori Makino

doi:10.1093/ptep/ptu084

E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach

Chaotic Dynamics 2022-08-23 v1 Quantum Physics

Authors: Hironori Makino

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Abstract

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.

Keywords

quantum level statistics classically integrable systems berry-robnik approach e(k,l) function level-spacing distribution poisson statistics

Cite

@article{arxiv.2208.09845,
  title  = {E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach},
  author = {Hironori Makino},
  journal= {arXiv preprint arXiv:2208.09845},
  year   = {2022}
}

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Published July 2014 in PTEP: https://academic.oup.com/ptep/article/2014/7/073A01/1562895. arXiv admin note: text overlap with arXiv:0902.1282

E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach

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