English

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