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On the Laplace operator with a weak magnetic field in exterior domains

Kachmar, Ayman LU ; Lotoreichik, Vladimir and Sundqvist, Mikael LU (2025) In Analysis and Mathematical Physics 15(1).
Abstract

We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper bound on the lowest eigenvalue in the weak field limit, involving the 4-moment, and optimal for the case of the disk. Moreover, we prove that, for moderate magnetic fields, the exterior of the disk is a local maximizer for the lowest eigenvalue under a p-moment constraint.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Eigenvalue asymptotics, Isoperimetric inequality, Landau levels, Magnetic Laplacian, Weak magnetic fields
in
Analysis and Mathematical Physics
volume
15
issue
1
article number
5
publisher
Springer Science and Business Media B.V.
external identifiers
  • scopus:85213570406
ISSN
1664-2368
DOI
10.1007/s13324-024-01001-1
language
English
LU publication?
yes
id
5673c478-1762-4b46-9a9b-58afdf011038
date added to LUP
2025-03-11 14:46:04
date last changed
2025-04-04 14:42:06
@article{5673c478-1762-4b46-9a9b-58afdf011038,
  abstract     = {{<p>We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper bound on the lowest eigenvalue in the weak field limit, involving the 4-moment, and optimal for the case of the disk. Moreover, we prove that, for moderate magnetic fields, the exterior of the disk is a local maximizer for the lowest eigenvalue under a p-moment constraint.</p>}},
  author       = {{Kachmar, Ayman and Lotoreichik, Vladimir and Sundqvist, Mikael}},
  issn         = {{1664-2368}},
  keywords     = {{Eigenvalue asymptotics; Isoperimetric inequality; Landau levels; Magnetic Laplacian; Weak magnetic fields}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Springer Science and Business Media B.V.}},
  series       = {{Analysis and Mathematical Physics}},
  title        = {{On the Laplace operator with a weak magnetic field in exterior domains}},
  url          = {{http://dx.doi.org/10.1007/s13324-024-01001-1}},
  doi          = {{10.1007/s13324-024-01001-1}},
  volume       = {{15}},
  year         = {{2025}},
}