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

Abstract

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.

19 pages, 4 figures

Cited by in corpus (1)

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