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

Hironori Makino, Nariyuki Minami

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Abstract

The theory of the quantal level statistics of a 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) [H. Makino and S. Tasaki, Phys. Rev. E 67, 066205 (2003); H. Makino and S. Tasaki, Prog. Theor. Phys. Suppl. 150, 376 (2003); H. Makino, N. Minami, and S. Tasaki, Phys. Rev. E 79, 036201 (2009); H.Makino and S. Tasaki, Prog. Theor. Phys. 114, 929 (2005)], is successfully extended to the study of the 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 ofMakino 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 [M. Robnik, Nonlinear Phenom. Complex Syst. 1, 1 (1998)]. We derive the limiting E(K, L) function in the limit of infinitely many components and elucidate its properties when energy levels show deviations from the Poisson statistics.

Original languageEnglish
Article number073A01
JournalProgress of Theoretical and Experimental Physics
Volume2014
Issue number7
DOIs
Publication statusPublished - 2014

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statistics
spacing
energy levels
deviation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "The theory of the quantal level statistics of a 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) [H. Makino and S. Tasaki, Phys. Rev. E 67, 066205 (2003); H. Makino and S. Tasaki, Prog. Theor. Phys. Suppl. 150, 376 (2003); H. Makino, N. Minami, and S. Tasaki, Phys. Rev. E 79, 036201 (2009); H.Makino and S. Tasaki, Prog. Theor. Phys. 114, 929 (2005)], is successfully extended to the study of the 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 ofMakino 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 [M. Robnik, Nonlinear Phenom. Complex Syst. 1, 1 (1998)]. We derive the limiting E(K, L) function in the limit of infinitely many components and elucidate its properties when energy levels show deviations from the Poisson statistics.",
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