Level statistics of systems with infinitely many independent components based on the Berry-Robnik approach

Details Level statistics of systems with infinitely many independent components based on the Berry-Robnik approach Level statistics of systems with infinitely many independent components based on the Berry-Robnik approach

2003-03-21

arxiv.org/abs/nlin/0303046v2

Nonlinear Sciences

Chaotic Dynamics

19 pages, 4 figures

Scientific paper

Along the line of thoughts of Berry and Robnik{\cite{Ber}}, the limiting gap distribution function of classically integrable quantum systems is derived in the limit of infinitely many independent components. The limiting gap distribution function is characterized by a single monotonically increasing function $\bar{\mu}(S)$ of the level spacing $S$, and the corresponding level spacing distribution is classified into three cases: (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 the energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.

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