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Abstract: We study a mixed heat and Schr\-odinger Ginzburg-Landau evolution equation ona bounded two-dimensional domain with an electric current applied on theboundary and a pinning potential term. This is meant to model a superconductorsubjected to an applied electric current and electromagnetic field andcontaining impurities. Such a current is expected to set the vortices inmotion, while the pinning term drives them toward minima of the pinningpotential and -pins- them there. We derive the limiting dynamics of a finitenumber of vortices in the limit of a large Ginzburg-Landau parameter, or $\ep\to 0$, when the intensity of the electric current and applied magnetic fieldon the boundary scale like $\lep$. We show that the limiting velocity of thevortices is the sum of a Lorentz force, due to the current, and a pinningforce. We state an analogous result for a model Ginzburg-Landau equationwithout magnetic field but with forcing terms. Our proof provides a unifiedapproach to various proofs of dynamics of Ginzburg-Landau vortices.



Autor: Sylvia Serfaty, Ian Tice

Fuente: https://arxiv.org/







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