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

H. Makino·S. Tasaki
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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 $\barμ(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\barμ(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\barμ(+\infty)< 1$, and (iii) sub-Poissonian if $\barμ(+\infty)=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.

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H. Makino, S. Tasaki. 2004-03-26. Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-. https://doi.org/10.1103/physreve.67.066205

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