The Laplacian with complex magnetic fields - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

The Laplacian with complex magnetic fields

Résumé

We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is relatively form-bounded with respect to the real part of the magnetic Laplacian, we introduce the operator as an m-sectorial operator. In two dimensions, sufficient conditions are established to guarantee that the resolvent is compact. In the case of non-critical complex magnetic fields, a WKB approach is used to construct semiclassical pseudomodes, which do not exist when the magnetic field is real-valued.
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Dates et versions

hal-04721413 , version 1 (04-10-2024)

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Identifiants

  • HAL Id : hal-04721413 , version 1

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David Krejcirik, Tho Nguyen Duc, Nicolas Raymond. The Laplacian with complex magnetic fields. 2024. ⟨hal-04721413⟩
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