Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach

Details Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach

2003-03-21

arxiv.org/abs/nlin/0303045v3

Progress of Theoretical Physics, Suppl. No 150, pp376-380(2003)

Nonlinear Sciences

Chaotic Dynamics

5 pages, 0 figure

Scientific paper

10.1143/PTPS.150.376

Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum systems. The level spacing distribution is classified into three cases: Case 1: Poissonian if $\bar{\mu}(+\infty)=0$, Case 2: Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and Case 3: sub-Poissonian if $\bar{\mu}(+\infty)=1$. Thus, even when the energy levels of individual components are statistically independent, non-Poisson level spacing distributions are possible.

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