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Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers

Miranda, Germán LU orcid (2024) In Journal of Mathematical Physics 65(7).
Abstract

The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-Noël et al. [Bull. London Math. Soc. 56, 2529 (2024)] to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
65
issue
7
article number
072101
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:85198920042
ISSN
0022-2488
DOI
10.1063/5.0208990
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2024 Author(s).
id
2289658b-b30c-41c8-ba8d-29bc27f8b06e
date added to LUP
2024-09-04 14:07:42
date last changed
2024-10-03 10:25:41
@article{2289658b-b30c-41c8-ba8d-29bc27f8b06e,
  abstract     = {{<p>The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-Noël et al. [Bull. London Math. Soc. 56, 2529 (2024)] to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.</p>}},
  author       = {{Miranda, Germán}},
  issn         = {{0022-2488}},
  language     = {{eng}},
  month        = {{07}},
  number       = {{7}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Journal of Mathematical Physics}},
  title        = {{Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers}},
  url          = {{http://dx.doi.org/10.1063/5.0208990}},
  doi          = {{10.1063/5.0208990}},
  volume       = {{65}},
  year         = {{2024}},
}