Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian

Details Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian

2008-06-27

arxiv.org/abs/0806.4513v1

Physics

Mathematical Physics

Scientific paper

We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhart domain we are able to show a more precise asymptotic formula.

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