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Symmetric superconducting states in thin films. (English) Zbl 0758.35075

Summary: Previous physical experiments and numerical studies suggest that, in the presence of a tangential external magnetic field, the density distribution of superconducting electron pairs and the excited field in a thin film are symmetric. In this paper, the existence of such symmetric solutions of the one-dimensional Ginzburg-Landau theory for thin film superconductivity is established. The behavior of these solutions versus the external field verifies the Meissner effect. At low fields, the classical London theory is recovered. The critical fields for extreme type II superconductors are higher than type I ones. Moreover, numerical examples calculated using a gradient-flow method for the reduced governing equations are presented which exhibit sharp phase transitions from the normal state to superconducting states or vice versa as one varies the applied field.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
82D55 Statistical mechanics of superconductors
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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