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arXiv · 2410.01377

The Laplacian with complex magnetic fields

David Krejcirik·Tho Nguyen Duc·Nicolas Raymond
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Abstract

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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David Krejcirik, Tho Nguyen Duc, Nicolas Raymond. 2024-10-02. The Laplacian with complex magnetic fields. https://arxiv.org/abs/2410.01377

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