Abstract:We consider the magnetic Schrödinger operator in the unit disk with constant magnetic field of strength $b>0$ and magnetic Neumann boundary condition. If $\lambda_1(b)$ denotes its lowest eigenvalue, then we prove that $\lambda_1(b) < \Theta_0 b$ for all $b>0$, where $\Theta_0$ 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.
| Comments: | 14 pages, 1 figure |
| Subjects: | Spectral Theory (math.SP) |
| Cite as: | arXiv:2605.24188 [math.SP] |
| (or arXiv:2605.24188v1 [math.SP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24188 arXiv-issued DOI via DataCite (pending registration) |
From: Mikael Sundqvist [view email]
[v1]
Fri, 22 May 2026 20:26:47 UTC (138 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。