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Clusters of eigenvalues for the magnetic Laplacian with Robin condition

Goffeng, Magnus; Kachmar, Ayman and Sundqvist, Mikael Persson LU (2016) In Journal of Mathematical Physics 57(6).
Abstract

We study the Schrödinger 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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
57
issue
6
publisher
American Institute of Physics
external identifiers
  • scopus:84977151340
  • wos:000379168200036
ISSN
0022-2488
DOI
10.1063/1.4954500
language
English
LU publication?
yes
id
5b441f97-36ec-4a86-bd1d-137da770e84d
date added to LUP
2017-01-25 15:01:08
date last changed
2017-10-22 05:25:34
@article{5b441f97-36ec-4a86-bd1d-137da770e84d,
  abstract     = {<p>We study the Schrödinger 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.</p>},
  articleno    = {063510},
  author       = {Goffeng, Magnus and Kachmar, Ayman and Sundqvist, Mikael Persson},
  issn         = {0022-2488},
  language     = {eng},
  month        = {06},
  number       = {6},
  publisher    = {American Institute of Physics},
  series       = {Journal of Mathematical Physics},
  title        = {Clusters of eigenvalues for the magnetic Laplacian with Robin condition},
  url          = {http://dx.doi.org/10.1063/1.4954500},
  volume       = {57},
  year         = {2016},
}