Spectral statistics in chaotic systems with a point interaction

Abstract

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.

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

References in corpus (2)

• Geometrical theory of diffraction and spectral statistics
• Universality in quantum parametric correlations

Cited by in corpus (5)

• Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems
• Spectral Statistics of Rectangular Billiards with Localized Perturbations
• Semiclassical universality of parametric spectral correlations
• Spectral statistics of nearly unidirectional quantum graphs
• Localized Perturbations of Integrable Systems