The Laplacian with complex magnetic fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911158456287232 |
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| author | Krejcirik, David Duc, Tho Nguyen Raymond, Nicolas |
| author_facet | Krejcirik, David Duc, Tho Nguyen Raymond, Nicolas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Laplacian with complex magnetic fields Krejcirik, David Duc, Tho Nguyen Raymond, Nicolas Mathematical Physics Functional Analysis Spectral Theory 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. |
| title | The Laplacian with complex magnetic fields |
| topic | Mathematical Physics Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2410.01377 |