Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-

Abstract

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function $\bar{\mu }(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu }(+\infty )=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu }(+\infty )<1$, and (iii) sub-Poissonian if $\bar{\mu }(+\infty )=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.

19 pages, 4 figures. Accepted for publication in Phys. Rev. E