Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916847038758912 |
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| author | Baur, Matthias |
| author_facet | Baur, Matthias |
| contents | We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field in a wide range of field strengths. Adapting an approach by Antunes and Freitas, we use gradient descent for the minimization procedure together with the Method of Fundamental solutions for eigenvalue computation. Remarkably, we observe that when the magnetic flux exceeds the index of the target eigenvalue, the minimizer is always a disk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field Baur, Matthias Optimization and Control Mathematical Physics Analysis of PDEs Spectral Theory 35Q40, 49Q10, 35P15 We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field in a wide range of field strengths. Adapting an approach by Antunes and Freitas, we use gradient descent for the minimization procedure together with the Method of Fundamental solutions for eigenvalue computation. Remarkably, we observe that when the magnetic flux exceeds the index of the target eigenvalue, the minimizer is always a disk. |
| title | Numerical Optimization of Eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field |
| topic | Optimization and Control Mathematical Physics Analysis of PDEs Spectral Theory 35Q40, 49Q10, 35P15 |
| url | https://arxiv.org/abs/2412.06533 |