Study of Spectral Statistics of Classically Integrable Systems

Details Study of Spectral Statistics of Classically Integrable Systems Study of Spectral Statistics of Classically Integrable Systems

2000-03-24

arxiv.org/abs/nlin/0003049v1

Nonlinear Sciences

Chaotic Dynamics

5 pages, 4 figures, PTP LaTeX style, to be published in the proceedings of the conference/summer school 'Let's Face Chaos thro

Scientific paper

10.1143/PTPS.139.544

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$, where $T_0$ is the period of the shortest periodic orbit of the system, however $L_{\rm max} \to \infty$ when $E \to \infty$.

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