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

摘要

We establish an asymptotic estimate of the lowest eigenvalue mu (bF). of the Schrodinger operator -del(bF)(2) with a magnetic. field in a. bounded 2-dimensional domain, where curl 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. [References: 33]