Magnetic Dirichlet Laplacian on a perturbed twisted tube
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909992060190720 |
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| author | Barseghyan, Diana Blaya, Ricardo Abreu Bory-Reyes, Juan Schneider, Baruch |
| author_facet | Barseghyan, Diana Blaya, Ricardo Abreu Bory-Reyes, Juan Schneider, Baruch |
| contents | It is well known that the spectrum of the Dirichlet Laplacian for a compact perturbation of a three-dimensional, periodically twisted tube is unstable with respect to domain deformations. This means that if the periodically twisted tube is unperturbed, then the spectrum of the Dirichlet Laplacian is purely essential. On the other hand, the perturbation of this domain produces eigenvalues below the essential spectrum. This paper considers the Dirichlet-Laplace operator with a magnetic field. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small and local deformations of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magnetic Dirichlet Laplacian on a perturbed twisted tube Barseghyan, Diana Blaya, Ricardo Abreu Bory-Reyes, Juan Schneider, Baruch Spectral Theory Functional Analysis It is well known that the spectrum of the Dirichlet Laplacian for a compact perturbation of a three-dimensional, periodically twisted tube is unstable with respect to domain deformations. This means that if the periodically twisted tube is unperturbed, then the spectrum of the Dirichlet Laplacian is purely essential. On the other hand, the perturbation of this domain produces eigenvalues below the essential spectrum. This paper considers the Dirichlet-Laplace operator with a magnetic field. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small and local deformations of the domain. |
| title | Magnetic Dirichlet Laplacian on a perturbed twisted tube |
| topic | Spectral Theory Functional Analysis |
| url | https://arxiv.org/abs/2601.10924 |