Statistical properties of spectral fluctuations for a quantum system with infinitely many components
arXiv:0902.1282 · doi:10.1103/PhysRevE.79.036201
Abstract
Extending the idea formulated in Makino {\it{et al}}[Phys.Rev.E {\bf{67}},066205], that is based on the Berry--Robnik approach [M.V. Berry and M. Robnik, J. Phys. A {\bf{17}}, 2413], 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 {\bf 43}, 5694].
6 figures, 10 pages
References in corpus (6)
- Quantum localization in rough billiards
- Quantum Surface of Section Method: Eigenstates and Unitary Quantum Poincare Evolution
- Mode fluctuations as fingerprint of chaotic and non-chaotic systems
- Comment on Energy Level Statistics in the Mixed Regime
- Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-
- Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--