具有钉扎和强外加电流的Ginzburg-Landau涡旋动力学
Ginzburg-Landau vortex dynamics with pinning and strong applied currents
摘要：
研究了二维有界区域上的混合热和薛定谔Ginzburg-Landau发展方程，其中边界上有电流和钉扎势项.这意味着要模拟一个受外加电流和电磁场影响并含有杂质的超导体。这样的电流预计将使涡旋运动，而钉扎项将它们推向钉扎电位的最小值并将它们“钉扎”在那里。当电流强度和外加磁场强度在边界尺度上类似于$\lep$时，我们导出了在大金斯堡-朗道参数或$\ep \to 0$的极限下有限个涡旋的极限动力学。我们表明，涡的极限速度是一个洛伦兹力的总和，由于电流，和钉扎力。本文对一个无磁场但有强迫项的模型Ginzburg-Landau方程给出了类似的结果。我们的证明提供了一个统一的方法来证明金兹伯格-朗道涡的动力学。
英文摘要：
We study a mixed heat and Schrödinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number 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 field on the boundary scale like $\lep$. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Ginzburg-Landau vortices.
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