Magnetic Dirichlet Laplacian in curved waveguides
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866909517303775232 |
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| author | Barseghyan, Diana Bernstein, Swanhild Schneider, Baruch Zimmermann, Martha Lina |
| author_facet | Barseghyan, Diana Bernstein, Swanhild Schneider, Baruch Zimmermann, Martha Lina |
| contents | For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable. Any perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, a magnetic field is added. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic Dirichlet Laplacian in curved waveguides Barseghyan, Diana Bernstein, Swanhild Schneider, Baruch Zimmermann, Martha Lina Spectral Theory Functional Analysis For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable. Any perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, a magnetic field is added. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide. |
| title | Magnetic Dirichlet Laplacian in curved waveguides |
| topic | Spectral Theory Functional Analysis |
| url | https://arxiv.org/abs/2502.21247 |