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Updated: Jun 23, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Statistical properties of spectral fluctuations for a quantum system with infinitely many components
1Department of Human and Information Science, Tokai University, 1117 Kitakaname, Hiratsuka-shi, Kanagawa 259-1292, Japan. makino@tokai-u.jp
Abstract:
Extending the idea formulated in Makino [Phys. Rev. E 67, 066205 (2003)], that is based on the Berry-Robnik approach [M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984)], 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 [D. Biswas, M. Azam, and S. V. Lawande, Phys. Rev. A 43, 5694 (1991)].
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