In this paper, we analyze the 'singular statistics' of pseudointegrable Šeba billiards, i.e. billiards perturbed by zero-range perturbations. We have shown that the computation of a spectrum is reduced to the calculation of the uniquely defined renormalized Green's function. We relate a spectrum of the billiard to the scattering length, which is the only parameter describing the perturbation. We show that taking into account the growing number of resonances, one observes a transition from 'semi-Poissonian'-like statistics to Poissonian. This observation is in agreement with the argument that a classical particle does not feel a point perturbation. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
CITATION STYLE
Tudorovskiy, T., Kuhl, U., & Stöckmann, H. J. (2010). Singular statistics revised. New Journal of Physics, 12. https://doi.org/10.1088/1367-2630/12/12/123021
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