Study of Spectral Statistics of Classically Integrable Systems

Marko Robnik; Gregor Veble

doi:10.1143/PTPS.139.544

paper

Study of Spectral Statistics of Classically Integrable Systems

arXiv:nlin/0003049 · doi:10.1143/PTPS.139.544

Abstract

In this work we present the results of a study of spectral statistics for a classically integrable system, namely the rectangle billiard. We show that the spectral statistics are indeed Poissonian in the semiclassical limit for almost all such systems, the exceptions being the atypical rectangles with rational squared ratio of its sides, and of course the energy ranges larger than L_{\rm max}=\hbar / T_0 $, w h er e$ T_0 $i s t h e p er i o d o f t h es h or t es tp er i o d i cor bi t o f t h esy s t e m, h o w e v er$ L_{\rm max} \to \infty $w h e n$ E \to \infty$.

5 pages, 4 figures, PTP LaTeX style, to be published in the proceedings of the conference/summer school 'Let's Face Chaos through Nonlinear Dynamics', Maribor, Slovenia, June/July 1999, eds. M. Robnik et al., Prog. Theor. Phys. Suppl. (Kyoto) 139 (2000)

References in corpus (1)

Regular and Irregular States in Generic Systems

Cited by in corpus (1)

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