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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.24188 |
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| _version_ | 1866911710816763904 |
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| author | Léna, Corentin Sundqvist, Mikael |
| author_facet | Léna, Corentin Sundqvist, Mikael |
| contents | We consider the magnetic Schrödinger operator in the unit disk with constant magnetic field of strength $b>0$ and magnetic Neumann boundary condition. If $λ_1(b)$ denotes its lowest eigenvalue, then we prove that $λ_1(b) < Θ_0 b$ for all $b>0$, where $Θ_0$ is the de Gennes constant. The proof has two parts, both based on Rayleigh's principle. For large $b$, we use a trial state built from the de Gennes ground state. For the remaining bounded range of $b$, we divide the interval into finitely many overlapping subintervals and, on each of them, choose a trial state from a finite-dimensional space. This reduces the proof to finitely many inequalities between rational numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A magnetic eigenvalue bound in the disk Léna, Corentin Sundqvist, Mikael Spectral Theory We consider the magnetic Schrödinger operator in the unit disk with constant magnetic field of strength $b>0$ and magnetic Neumann boundary condition. If $λ_1(b)$ denotes its lowest eigenvalue, then we prove that $λ_1(b) < Θ_0 b$ for all $b>0$, where $Θ_0$ is the de Gennes constant. The proof has two parts, both based on Rayleigh's principle. For large $b$, we use a trial state built from the de Gennes ground state. For the remaining bounded range of $b$, we divide the interval into finitely many overlapping subintervals and, on each of them, choose a trial state from a finite-dimensional space. This reduces the proof to finitely many inequalities between rational numbers. |
| title | A magnetic eigenvalue bound in the disk |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2605.24188 |