Point perturbations of circle billiards

Details Point perturbations of circle billiards Point perturbations of circle billiards

2003-09-23

arxiv.org/abs/nlin/0309061v1

J. Phys. A: Math. Gen., v36, L529 (2003)

Nonlinear Sciences

Chaotic Dynamics

9 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/40/L02

The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which the scatterer is located in the classically forbidden region and its energy levels are not affected by the scatterer in the semiclassical limit while the second sequence contains the levels which are affected by the point-scatterer. The nearest neighbor spacing distribution which results from the superposition of these sequences is calculated analytically within some approximation and good agreement with the distribution that was computed numerically is found.

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