Consolidating boundary methods for finding the eigenstates of billiards
Chaotic Dynamics
2009-11-07 v3 Condensed Matter
Abstract
The plane-wave decomposition method (PWDM), a widely used means of numerically finding eigenstates of the Helmholtz equation in billiard systems is described as a variant of the mathematically well-established boundary integral method (BIM). A new unified framework encompassing the two methods is discussed. Furthermore, a third numerical method, which we call the Gauge Freedom Method (GFM) is derived from the BIM equations. This opens the way to further improvements in eigenstate search techniques.
Cite
@article{arxiv.nlin/0108014,
title = {Consolidating boundary methods for finding the eigenstates of billiards},
author = {Doron Cohen and Natasha Lepore and Eric J. Heller},
journal= {arXiv preprint arXiv:nlin/0108014},
year = {2009}
}
Comments
24 pages, 9 figures, textual improvements