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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06411 |
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| _version_ | 1866913384110227456 |
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| author | Fournais, Soeren Kachmar, Ayman |
| author_facet | Fournais, Soeren Kachmar, Ayman |
| contents | For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component and a Dirichlet condition on the other, one gets fewer such eigenvalues than when imposing Neumann boundary conditions on the two components. We quantify this observation for two models: the strip and the annulus. In both models one can separate variables and deal with a family of fiber operators, thereby reducing the problem to counting band functions, the eigenvalues of the fiber operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting eigenvalues below the lowest Landau level Fournais, Soeren Kachmar, Ayman Spectral Theory For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component and a Dirichlet condition on the other, one gets fewer such eigenvalues than when imposing Neumann boundary conditions on the two components. We quantify this observation for two models: the strip and the annulus. In both models one can separate variables and deal with a family of fiber operators, thereby reducing the problem to counting band functions, the eigenvalues of the fiber operators. |
| title | Counting eigenvalues below the lowest Landau level |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2406.06411 |