1996/02/29 by P. Rosenqvist, P Rosenqvist, N. D. Whelan +3 · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #chao-dyn #nlin.CD
paper · pdf · doi:10.1088/0305-4470/29/17/018
published as J. Phys. A: Math. Gen. 29 no. 17 (1996) 5441-5453 · Final published version - some changes in the discussion and the labels on one figure are corrected
openalex publication_date 1996/09/07 · arxiv created 1996/09/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit expansion. This situation is formally similar to edge diffraction except that the disk radii introduce a length scale in the problem such that for wavelengths smaller than the order of the disk radius we recover the usual semiclassical approximation; however, for wavelengths larger than the order of the disk radius there is a qualitatively different behaviour. We test the theory by successfully estimating the positions of scattering resonances in geometries consisting of three and four small disks.