Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains

Pan, Xing-Bin; Kwek, Keng-Huat

doi:10.1090/S0002-9947-02-03033-7

Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains
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by Xing-Bin Pan and Keng-Huat Kwek PDF

Trans. Amer. Math. Soc. 354 (2002), 4201-4227 Request permission

Abstract:

We establish an asymptotic estimate of the lowest eigenvalue $\mu (b\mathbf {F})$ of the Schrödinger operator $-\nabla _{b\mathbf {F}}^{2}$ with a magnetic field in a bounded $2$-dimensional domain, where curl $\mathbf {F}$ vanishes non-degenerately, and $b$ is a large parameter. Our study is based on an analysis on an eigenvalue variation problem for the Sturm-Liouville problem. Using the estimate, we determine the value of the upper critical field for superconductors subject to non-homogeneous applied magnetic fields, and localize the nucleation of superconductivity.

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