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 2π 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.
Publié le : 1995-07-05
Classification:
quantum billiards,
inside-outside duality,
scattering theory,
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
@article{hal-00129121,
author = {Pillet, Claude-Alain and Eckmann, Jean-Pierre and Dietz, Barbara and Smilansky, Uzy and Ussishkin, Iddo},
title = {Inside-outside duality for planar billiards: A numerical study},
journal = {HAL},
volume = {1995},
number = {0},
year = {1995},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00129121}
}
Pillet, Claude-Alain; Eckmann, Jean-Pierre; Dietz, Barbara; Smilansky, Uzy; Ussishkin, Iddo. Inside-outside duality for planar billiards: A numerical study. HAL, Tome 1995 (1995) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129121/