Effective operators on an attractive magnetic edge

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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
Pages (from-to)917-944
Number of pages28
Publication statusPublished - 2023

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

    Research areas

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

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