2003/03/21 by H. Makino, Makino, H., S. Tasaki +1
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0303046
19 pages, 4 figures
arxiv created 2004/03/26 · arxiv updated 2009/11/30
Along the line of thoughts of Berry and Robnik\citeBer, 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 μ(S) of the level spacing S, and the corresponding level spacing distribution is classified into three cases: (i) Poissonian if μ(+∞)=0, (ii) Poissonian for large S, but possibly not for small S if 0<μ(+∞)< 1, and (iii) sub-Poissonian if μ(+∞)=1. This implies that even when the energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.