Semiclassical level spacings when regular and chaotic orbits coexist

Abstract

The authors calculate semiclassical limiting level spacing distributions P(S) for systems whose classical energy surface is divided into a number of separate region in which motion is regular or chaotic. In the calculation it is assumed that the spectrum is the superposition of statistically independent sequences of levels from each of the classical phase-space regions, sequences from regular regions, having Poisson distributions and those from irregular regions having Wigner distributions. The formulae for P(S) depend on the sum of the Liouville measures of all the classical regular regions, and on the separate Liouville measures of the significant chaotic regions.