Effective operators on an attractive magnetic edge

Soren Fournais, Bernard Helffer, Ayman Kachmar, Nicolas Raymond

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3 Citations (Scopus)
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Abstract

The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.

Original languageEnglish
JournalJournal de l'Ecole Polytechnique - Mathematiques
Volume10
Pages (from-to)917-944
Number of pages28
ISSN2429-7100
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Ecole Polytechnique. All rights reserved.

Keywords

  • discontinuous magnetic field
  • Magnetic Laplacian
  • semiclassical analysis
  • spectrum

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