Polya's conjecture in the presence of a constant magnetic field
Mathematical Physics
2007-10-05 v1 math.MP
Abstract
We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Polya's conjecture is not true in the presence of a magnetic field.
Keywords
Cite
@article{arxiv.0710.1078,
title = {Polya's conjecture in the presence of a constant magnetic field},
author = {Rupert L. Frank and Michael Loss and Timo Weidl},
journal= {arXiv preprint arXiv:0710.1078},
year = {2007}
}
Comments
15 pages