1999/05/24 by Saar Rahav, Rahav, Saar, Oded Agam +3
Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9905037
15 pages, 1 figure
arxiv created 1999/05/24 · openalex publication_date 1999/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.