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The magnetic Laplacian on the disc for strong magnetic fields

Kachmar, Ayman LU and Miranda, Germán LU orcid (2025) In Journal of Mathematical Analysis and Applications 546(2).
Abstract

The magnetic Laplacian on a planar domain under a strong constant magnetic field has eigenvalues close to the Landau levels. We study the case when the domain is a disc and the spectrum consists of branches of eigenvalues of one dimensional operators. Under Neumann boundary condition and strong magnetic field, we derive asymptotics of the eigenvalues with accurate estimates of exponentially small remainders. Our approach is purely variational and applies to the Dirichlet boundary condition as well, which allows us to recover recent results by Baur and Weidl.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Branches of eigenvalues, Magnetic Laplacian, Semi-classical approximation, Temple's inequality
in
Journal of Mathematical Analysis and Applications
volume
546
issue
2
article number
129261
publisher
Academic Press
external identifiers
  • scopus:85215207277
ISSN
0022-247X
DOI
10.1016/j.jmaa.2025.129261
language
English
LU publication?
yes
id
6bf9ebe8-89d7-4e36-a727-4ab88b4129d4
date added to LUP
2025-03-17 14:48:44
date last changed
2025-04-04 14:19:13
@article{6bf9ebe8-89d7-4e36-a727-4ab88b4129d4,
  abstract     = {{<p>The magnetic Laplacian on a planar domain under a strong constant magnetic field has eigenvalues close to the Landau levels. We study the case when the domain is a disc and the spectrum consists of branches of eigenvalues of one dimensional operators. Under Neumann boundary condition and strong magnetic field, we derive asymptotics of the eigenvalues with accurate estimates of exponentially small remainders. Our approach is purely variational and applies to the Dirichlet boundary condition as well, which allows us to recover recent results by Baur and Weidl.</p>}},
  author       = {{Kachmar, Ayman and Miranda, Germán}},
  issn         = {{0022-247X}},
  keywords     = {{Branches of eigenvalues; Magnetic Laplacian; Semi-classical approximation; Temple's inequality}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Mathematical Analysis and Applications}},
  title        = {{The magnetic Laplacian on the disc for strong magnetic fields}},
  url          = {{http://dx.doi.org/10.1016/j.jmaa.2025.129261}},
  doi          = {{10.1016/j.jmaa.2025.129261}},
  volume       = {{546}},
  year         = {{2025}},
}