2000/12/31 by Stefan Keppeler
Mathematics · Physics and Astronomy · #Consistency (knowledge bases) #Distribution (mathematics) #Eigenvalues and eigenvectors #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Periodic orbits #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Representation (politics) #Scientific Research and Discoveries #Semiclassical physics #Statistics #Stochastic processes and statistical mechanics #TRACE (psycholinguistics) #nlin.CD
paper · pdf · doi:10.1103/physreve.64.027201
published as Phys. Rev. E 64 (2001) 027201 · 4 pages, 2 figures; major revisions in the second part, range of validity of asymptotic evaluation clarified
arxiv created 2001/03/15 · openalex publication_date 2001/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this representation for the nearest-neighbor level spacing (k=0). In a second part, we present an asymptotic evaluation for large spacings, where consistency with random matrix theory is achieved for large k. We also discuss the relation with the method of Bogomolny and Keating [Phys. Rev. Lett. 77, 1472 (1996)] for two-point correlations.