Geometric Phase in Quantum Billiards with a Pointlike Scatterer
High Energy Physics - Theory
2009-10-28 v1 chao-dyn
Chaotic Dynamics
Nuclear Theory
Quantum Physics
Abstract
We examine the quantum energy levels of rectangular billiards with a pointlike scatterer in one and two dimensions. By varying the location and the strength of the scatterer, we systematically find diabolical degeneracies among various levels. The associated Berry phase is illustrated, and the existence of localized wave functions is pointed out. In one dimension, even the ground state is shown to display the sign reversal with a mechanism to circumvent the Sturm-Liouville theorem.
Cite
@article{arxiv.hep-th/9512164,
title = {Geometric Phase in Quantum Billiards with a Pointlike Scatterer},
author = {Taksu Cheon and Takaomi Shigehara},
journal= {arXiv preprint arXiv:hep-th/9512164},
year = {2009}
}
Comments
9 pages, RevTex file, 6 postscript figures (gz compressed), uuencoded