Spectral statistics in chaotic systems with a point interaction

Details Spectral statistics in chaotic systems with a point interaction Spectral statistics in chaotic systems with a point interaction

2000-03-08

arxiv.org/abs/nlin/0003019v2

J. Phys. A 33 (2000) 6263

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 21 pages, 7 figures, small corrections, new references added

Scientific paper

10.1088/0305-4470/33/36/301

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order tau^2 and tau^3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.

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