2008/04/10 by B. Dietz, Barbara Dietz, Bernhard Mößner +5
Mathematics · Physics and Astronomy · #Ball (mathematics) #Chaos control and synchronization #Chaotic #Classical mechanics #Dynamical billiards #Eigenvalues and eigenvectors #Geometry #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Random matrix #Scientific Research and Discoveries #Symmetry (geometry) #Symmetry breaking #nlin.CD
paper · pdf · doi:10.1103/physreve.77.046221
published as Phys. Rev. E 77, 046221 (2008) · 11 pages, 10 eps figures
arxiv created 2008/04/10 · openalex publication_date 2008/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees and it is classically chaotic. The billiard exhibits only a few families of nongeneric periodic orbits. We introduce an analytic method for their treatment. The length spectrum can be understood in terms of the nongeneric and unstable periodic orbits. For unequal radii of the quarter cylinders the level statistics agree well with predictions from random matrix theory. For equal radii the billiard exhibits an additional symmetry. We investigated the effects of symmetry breaking on spectral properties. Moreover, for equal radii, we observe a small deviation of the level statistics from random matrix theory. This led to the discovery of stable and marginally stable orbits, which are absent for unequal radii.