Vortex dynamics in the Ginzburg-Landau and Maxwell-Klein-Gordon models with pinning - Wileman, Paul (2021)
We study the motion of vortices in a superconductor subject to a perturbed background potential. Such a potential models the presence of pinning sites in the superconductor which the vortices are attracted to. The pinning potential is scaled such that the intervortex interactions also play a role in the vortex dynamics. We use the time-dependent Ginzburg-Landau model to relate the vortex velocities to forces in the system; namely, the gradient of the renormalized energy which accounts for intervortex interactions and the gradient of the pinning potential. We make an effort to include the gauge terms at every step. Additionally, we include both parabolic motion and Schrodinger flow from the outset which results in a mixed-flow dynamical law.