On Duclos–Exner’s conjecture about waveguides in strong uniform magnetic fields

We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition on the width and the curvature of the strip ensuring the existence of the discrete spectrum in the strong magnetic field limit, answering (negatively) a conjecture made...

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Bibliographic Details
Published in:Forum of mathematics. Sigma 2023-01, Vol.11, Article e11
Main Authors: Bon-Lavigne, Enguerrand, Le Treust, Loïc, Raymond, Nicolas, Royer, Julien
Format: Article
Language:English
Subjects:
35P15
81Q10
Boundary conditions
Dirichlet problem
Magnetic fields
Mathematical Physics
Mathematics
Strip
Waveguides
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Summary:We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition on the width and the curvature of the strip ensuring the existence of the discrete spectrum in the strong magnetic field limit, answering (negatively) a conjecture made by Duclos and Exner.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2023.9