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

H. Makino, Nariyuki Minami, S. Tasaki

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Article number036201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number3
DOIs
Publication statusPublished - 2009 Mar 3

Fingerprint

Quantum Systems
Statistical property
Fluctuations
Siméon Denis Poisson
statistics
Quantum Integrable Systems
Statistics
spectral correlation
Torus Action
Semiclassical Limit
Periodic Orbits
Superposition
Slope
Deviation
Limiting
slopes
orbits
deviation

ASJC Scopus subject areas

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

Cite this

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