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COUNTING NEGATIVE EIGENVALUES FOR THE MAGNETIC PAULI OPERATOR

Fournais, SØren ; Frank, Rupert L. ; Goffeng, Magnus LU orcid ; Kachmar, Ayman and Sundqvist, Mikael (2025) In Duke Mathematical Journal 174(2). p.313-353
Abstract

We study the Pauli operator in a 2-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower bound to obtain a new formula on the number of eigenvalues of the magnetic Neumann Laplacian in the semiclassical limit. Our approach relies on reduction to a boundary Dirac operator. We analyze this boundary operator in two different ways. The first approach uses Atiyah-Patodi-Singer (APS) index theory. The second approach relies on a conservation law for the Benjamin-Ono equation.

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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Duke Mathematical Journal
volume
174
issue
2
pages
41 pages
publisher
Duke University Press
external identifiers
  • scopus:86000173886
ISSN
0012-7094
DOI
10.1215/00127094-2024-0029
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 Duke University Press. All rights reserved.
id
8918da05-4a1c-4b0c-9bf6-c2f78f67c81a
date added to LUP
2025-06-23 12:49:57
date last changed
2025-06-27 09:38:32
@article{8918da05-4a1c-4b0c-9bf6-c2f78f67c81a,
  abstract     = {{<p>We study the Pauli operator in a 2-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower bound to obtain a new formula on the number of eigenvalues of the magnetic Neumann Laplacian in the semiclassical limit. Our approach relies on reduction to a boundary Dirac operator. We analyze this boundary operator in two different ways. The first approach uses Atiyah-Patodi-Singer (APS) index theory. The second approach relies on a conservation law for the Benjamin-Ono equation.</p>}},
  author       = {{Fournais, SØren and Frank, Rupert L. and Goffeng, Magnus and Kachmar, Ayman and Sundqvist, Mikael}},
  issn         = {{0012-7094}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{313--353}},
  publisher    = {{Duke University Press}},
  series       = {{Duke Mathematical Journal}},
  title        = {{COUNTING NEGATIVE EIGENVALUES FOR THE MAGNETIC PAULI OPERATOR}},
  url          = {{http://dx.doi.org/10.1215/00127094-2024-0029}},
  doi          = {{10.1215/00127094-2024-0029}},
  volume       = {{174}},
  year         = {{2025}},
}