1999/01/01 by Bambi Hu, Baowen Li, Daniel C Rouben · 3 citations
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Conformal map #Dynamical billiards #Eigenvalues and eigenvectors #Integrable system #Numerical methods for differential equations #Quantization (signal processing) #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Semiclassical physics #chao-dyn #cond-mat #nlin.CD #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/29/303
published in Journal of Physics A Mathematical and General 32(29), 5419-5433 (Institute of Physics) · 21 Revtex pages, 6 ps figures, accepted for publication in J. Phys. A
openalex publication_date 1999/01/01 · arxiv created 1999/06/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use the semiclassical quantization scheme of Bogomolny to calculate eigenvalues of the Limaçon quantum billiard corresponding to a conformal map of the circle billiard. We use the entire billiard boundary as the chosen surface of section and use a finite approximation for the transfer operator in coordinate space. Computation of the eigenvalues of this matrix combined with a quantization condition, determines a set of semiclassical eigenvalues which are compared with those obtained by solving the Schrödinger equation. The classical dynamics of this billiard system undergoes a smooth transition from integrable (circle) to completely chaotic motion, thus providing a test of Bogomolny's semiclassical method in coordinate space in terms of the morphology of the wavefunction. We analyse the results for billiards which exhibit both soft and hard chaos.