Vortex Motion in Ginzburg-Landau Equations with Background Potentials and Thermal Fluctuations

Abstract

In this work, we investigate several models of superconductivity and the motion of vortices within them. We introduce anonisothermal model that incorporates thermal fluctuations away from a critical temperature and prove global well-posedness of weak solutions in the physically relevant setting. We then prove a motion law for systems with time-dependent background potentials in terms of a simple system of ordinary differential equations. Finally, we numerically investigate the convergence of simulated vortices to these motion laws and use the motion law for time-dependent potentials to develop a heuristic for use in nonisothermal systems.