Polya's conjecture in the presence of a constant magnetic field

Details Polya's conjecture in the presence of a constant magnetic field Polya's conjecture in the presence of a constant magnetic field

2007-10-04

arxiv.org/abs/0710.1078v1

Physics

Mathematical Physics

15 pages

Scientific paper

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.

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