Eigenvalues of \v{S}eba billiards with localization of low-energy eigenfunctions
Mathematical Physics
2016-01-22 v5 math.MP
Spectral Theory
Quantum Physics
Abstract
We study the localization of eigenfunctions produced by a point scatterer on a thin rectangle. We find an explicit set of eigenfunctions localized to part of the rectangle by showing that the one-dimensional Schr\"odinger operator with a Dirac delta potential asymptotically governs the spectral properties of the two-dimensional point scatterer. We also find the rate of localization in terms of the aspect ratio of the rectangle. In addition, we present numerical results regarding the asymptotic behavior of the localization.
Keywords
Cite
@article{arxiv.1504.02138,
title = {Eigenvalues of \v{S}eba billiards with localization of low-energy eigenfunctions},
author = {Minjae Lee},
journal= {arXiv preprint arXiv:1504.02138},
year = {2016}
}
Comments
17 pages, 7 figures