Work

Inside-outside duality for planar billiards: A numerical study

Year: 1995

Type: article

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, which is, basically, that every energy at which a scattering phase is 2\ensuremath{\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.

Source: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

DOI: 10.1103/physreve.51.4222

Authors: Barbara Dietz, Jean-Pierre Eckmann, Claude-Alain Pillet, Uzy Smilansky, Iddo Ussishkin

Institutions: University of Geneva, Weizmann Institute of Science, Universidad Nacional Autónoma de México

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

OpenAlex ID: W1968359932

FWCI: 3.295

Cites: 10

Cited by: 25

Related to: 10