### Abstract

Extending the idea formulated in Makino [Phys. Rev. E 67, 066205 (2003)], that is based on the Berry-Robnik approach, we investigate the statistical properties of a two-point spectral correlation for a classically integrable quantum system. The eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit. We derive the level number variance (LNV) in the limit of infinitely many components and discuss its deviations from Poisson statistics. The slope of the limiting LNV is found to be larger than that of Poisson statistics when the individual components have a certain accumulation. This property agrees with the result from the semiclassical periodic-orbit theory that is applied to a system with degenerate torus actions.

Original language | English |
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Article number | 036201 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 79 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Mar 3 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

**Statistical properties of spectral fluctuations for a quantum system with infinitely many components.** / Makino, H.; Minami, Nariyuki; Tasaki, S.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 79, no. 3, 036201. https://doi.org/10.1103/PhysRevE.79.036201

}

TY - JOUR

T1 - Statistical properties of spectral fluctuations for a quantum system with infinitely many components

AU - Makino, H.

AU - Minami, Nariyuki

AU - Tasaki, S.

PY - 2009/3/3

Y1 - 2009/3/3

N2 - Extending the idea formulated in Makino [Phys. Rev. E 67, 066205 (2003)], that is based on the Berry-Robnik approach, we investigate the statistical properties of a two-point spectral correlation for a classically integrable quantum system. The eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit. We derive the level number variance (LNV) in the limit of infinitely many components and discuss its deviations from Poisson statistics. The slope of the limiting LNV is found to be larger than that of Poisson statistics when the individual components have a certain accumulation. This property agrees with the result from the semiclassical periodic-orbit theory that is applied to a system with degenerate torus actions.

AB - Extending the idea formulated in Makino [Phys. Rev. E 67, 066205 (2003)], that is based on the Berry-Robnik approach, we investigate the statistical properties of a two-point spectral correlation for a classically integrable quantum system. The eigenenergy sequence of this system is regarded as a superposition of infinitely many independent components in the semiclassical limit. We derive the level number variance (LNV) in the limit of infinitely many components and discuss its deviations from Poisson statistics. The slope of the limiting LNV is found to be larger than that of Poisson statistics when the individual components have a certain accumulation. This property agrees with the result from the semiclassical periodic-orbit theory that is applied to a system with degenerate torus actions.

UR - http://www.scopus.com/inward/record.url?scp=63249111087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63249111087&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.79.036201

DO - 10.1103/PhysRevE.79.036201

M3 - Article

AN - SCOPUS:63249111087

VL - 79

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 3

M1 - 036201

ER -