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Clusters of eigenvalues for the magnetic Laplacian with Robin condition

Journal article
Authors Magnus Goffeng
A. Kachmar
M. P. Sundqvist
Published in Journal of Mathematical Physics
Volume 57
Issue 6
Pages artikel nr 063510
ISSN 0022-2488
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Pages artikel nr 063510
Language en
Keywords schrodinger-operators, spectral asymptotics, edge states, Physics
Subject categories Mathematical physics, Geometry, Mathematical Analysis


We study the Schrodinger operator with a constant magnetic field in the exterior of a compact domain in Euclidean space. Functions in the domain of the operator are subject to a boundary condition of the third type (a magnetic Robin condition). In addition to the Landau levels, we obtain that the spectrum of this operator consists of clusters of eigenvalues around the Landau levels and that they do accumulate to the Landau levels from below. We give a precise asymptotic formula for the rate of accumulation of eigenvalues in these clusters, which is independent of the boundary condition. Published by AIP Publishing.

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