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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.
A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics whereas those of time-reversal symmetric, classically cha
The structure of the semiclassical trace formula can be used to construct a quasi-classical evolution operator whose spectrum has a one-to-one correspondence with the semiclassical quantum spectrum. We illustrate this for marginally unstable integrab
In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the
The dynamics of a beam held on a horizontal frame by springs and bouncing off a step is described by a separable two degrees of freedom Hamiltonian system with impacts that respect, point wise, the separability symmetry. The energy in each degree of
Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing di