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

2003/03/21 by H. Makino, Hironori Makino, Makino, H. +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Berry #Chaotic Dynamics (nlin.CD) #Computer science #Econometrics #FOS: Physical sciences #Mathematical Control Systems and Analysis #Mathematics #Scientific Research and Discoveries #Statistical and Computational Modeling #Statistics #nlin.CD

paper · pdf · doi:10.48550/arxiv.nlin/0303046

published in arXiv (Cornell University) (Cornell University) · 19 pages, 4 figures

openalex publication_date 2003/03/21 · arxiv created 2004/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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

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