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

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 (mu) over bar (S) of the level spacing S. Three cases are distinguished: (1) Poissonian if (mu) over bar(+infinity)=0, (2) Poissonian for large S, but possibly not for small S if 0 < (mu) over bar(+infinity)<1, and (3) sub-Poissonian if (mu) over bar(+infinity)=1. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.