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Statistics of energy spectra are studied for quantum billiards, i.e., free motion of a particle in two dimensions surrounded by a hard wall. The transition from regular to irregular spectra observed in moments of nearest-neighbor spacing distributions for different shapes of the boundary is analyzed by a superposition of independent level sequences with Poisson and Wigner distributions. The rate of mixture of the two sequences is compared with the rate of phase volumes spanned by quasiperiodic and chaotic orbits of the corresponding classical motion.
Ishikawa et al. (Mon,) studied this question.