Long-Range Spectral Statistics of Classically Integrable Systems: Investigation along the Line of the Berry-Robnik Approach

Extending the argument of Ref.\citen{[4]} to the long-range spectralstatistics of classically integrable quantum systems, we examine the levelnumber variance, spectral rigidity and two-level cluster function. Theseobservables are obtained by applying the approach of Berry and Robnik\cite{[0]}and the mathematical framework of Pandey \cite{[2]} to systems with infinitelymany components, and they are parameterized by a single function $\bar{c}$,where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$indicates deviations from Poisson statistics. This implies that even when thespectral components are statistically independent, non-Poissonian spectralstatistics are possible.Comment: 13 pages, 4 figure