PMID: 12786474Jun 6, 2003Paper

Evanescent wave approach to diffractive phenomena in convex billiards with corners

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Jan Wiersig, Gabriel G Carlo

Abstract

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper we use the well-known scaling quantization procedure to study them. We show how the scaling method can be applied to convex billiards with corners, taking into account the strong diffraction at them and the techniques needed to solve their Helmholtz equation. As an example, we study a classically pseudointegrable billiard, the truncated triangle. Then we focus our attention on the spectral behavior. A numerical study of the statistical properties of high-lying energy levels is carried out. It is found that all computed statistical quantities are roughly described by the so-called semi-Poisson statistics, but it is not clear whether the semi-Poisson statistics is the correct one in the semiclassical limit.

References

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Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Wiersig
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Citations

Oct 19, 2019·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Marcel Eichelmann, Jan Wiersig

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