Low rank perturbations and the spectral statistics of pseudointegrable billiards

Details Low rank perturbations and the spectral statistics of pseudointegrable billiards Low rank perturbations and the spectral statistics of pseudointegrable billiards

2003-03-18

arxiv.org/abs/nlin/0303034v2

Phys. Rev. E 68, 065205(R) (2003)

Nonlinear Sciences

Chaotic Dynamics

4 pages

Scientific paper

10.1103/PhysRevE.68.065205

We present an efficient method to solve Schr\"odinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. To illustrate the power of the method, we calculate the number variance for two pseudointegrable quantum billiards: the barrier billiard and the right triangle billiard (smallest angle $\pi/5$). In this way, we obtain precise estimates for the level compressibility in the semiclassical (high energy) limit. In both cases, our results confirm recent theoretical predictions, based on periodic orbit summation.

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