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Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. (English) Zbl 0814.34039
Summary: We study the dynamics of vortices in time-dependent Ginzburg-Landau theories in the asymptotic limit when the vortex core size is much smaller than the inter-vortex distance. We derive reduced systems of ODEs governing the evolution of these vortices. We then extend these to study the dynamics of vortices in extremely type-II superconductors. Dynamics of vortex lines is also considered. For the simple Ginzburg-Landau equation without the magnetic field, we find that the vortices are stationary in the usual diffusive scaling, and obey remarkably simple dynamic laws when time is speeded up by a logarithmic factor. For columnar vortices in superconductors, we find a similar dynamic law with a potential which is screened by the current. For curved vortex lines in superconductors, we find that the vortex lines move in the direction of the normal with a speed proportional to the curvature. Comparisons are made with the previous results of John Neu.

34E05 Asymptotic expansions of solutions to ordinary differential equations
82D55 Statistical mechanical studies of superconductors
Full Text: DOI
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