Clusters of eigenvalues for the magnetic Laplacian with Robin condition
(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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https://lup.lub.lu.se/record/5b441f97-36ec-4a86-bd1d-137da770e84d
- author
- Goffeng, Magnus LU ; Kachmar, Ayman and Sundqvist, Mikael Persson LU
- organization
- publishing date
- 2016
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 57
- issue
- 6
- article number
- 063510
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- wos:000379168200036
- scopus:84977151340
- 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
- 2024-01-04 21:33:30
@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>}},
author = {{Goffeng, Magnus and Kachmar, Ayman and Sundqvist, Mikael Persson}},
issn = {{0022-2488}},
language = {{eng}},
number = {{6}},
publisher = {{American Institute of Physics (AIP)}},
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}},
doi = {{10.1063/1.4954500}},
volume = {{57}},
year = {{2016}},
}