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Effective dynamics of a magnetic vortex in a local potential. (English) Zbl 1106.78004

In this study, the authors investigate a simplified mean field model of superconductor dynamics in the presence of impurities or for variable superconductor depth. The model is expressed by the gradient flow-version of the Ginzburg-Landau equations, which are the standard equations for a superconductor in the mean field approximation in the temporal gauge, in the presence of a local potential. They determine a dynamical law of motion of the vortex center, involving the potential, such that for datum close to a (static) magnetic vortex the solution is always close to a magnetic vortex whose center obeys this law.

MSC:

78A30 Electro- and magnetostatics
78-02 Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
82D55 Statistical mechanics of superconductors
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