Inside-Outside Duality for Planar Billiards -- A Numerical Study

Abstract

This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close connection between eigenvalues of the billiard Laplacian and the scattering phases, basically that every energy at which a scattering phase is $2\pi$ corresponds to an eigenenergy of the Laplacian. Interesting phenomena appear when the shape of the domain does not allow an extension of the eigenfunction to the exterior. In this paper these phenomena are studied and illustrated from several points of view.

uuencoded tar-compressed (using uufiles) postscript file, 15 pages

References in corpus (1)

• Spectral Duality for Planar Billiards

Cited by in corpus (9)

• Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems
• GOE statistics in graphene billiards with the shape of classically integrable billiards
• Consolidating boundary methods for finding the eigenstates of billiards
• An efficient Fredholm method for calculation of highly excited states of billiards
• Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
• Inside-outside duality with artificial backgrounds
• Exterior-Interior Duality for Discrete Graphs
• Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards
• Duality of bounded and scattering wave systems with local symmetries