Spacing distributions for rhombus billiards

Details Spacing distributions for rhombus billiards Spacing distributions for rhombus billiards

1998-07-16

arxiv.org/abs/chao-dyn/9807022v1

Nonlinear Sciences

Chaotic Dynamics

9 pages (revtex) + 5 figures

Scientific paper

We show that the spacing distributions of rational rhombus billiards fall in a family of universality classes distinctly different from the Wigner-Dyson family of random matrix theory and the Poisson distribution. Some of the distributions find explanation in a recent work of Bogomolny, Gerland and Schmit. For the irrational billiards, despite ergodicity, we get the same distributions for the examples considered - once again, distinct from the Wigner-Dyson distributions. All results are obtained numerically by a method that allows us to reach very high energies.

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