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

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

1995-02-05

arxiv.org/abs/chao-dyn/9502003v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevE.51.4222

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.

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