Stochastic dynamics of Ginzburg-Landau vortices in superconductors

The phenomenological Ginzburg-Landau model for lowtemperature superconductivity has received much attention. However, it is not applicable to physical contexts that do not take into account factors such as material defects or thermal fluctuations. Thus, existing studies of the stability, dynamics, interactions, and other properties of the vortex state do not necessarily carry over to situations for which these factors cannot be ignored. The effects of defects and thermal fluctuations play a central role in the motion and pinning of vortices in type-II superconductors. In this Brief Report, we examine the vortex dynamics in type-II superconductors based on stochastic versions of the Ginzburg-Landau model. For simplicity, we assume that the underlying material sample possesses a large value for the Ginzburg-Landau parameter k so that a reduction of the Ginzburg-Landau equations to their high-k limit can be employed. In this case, the given applied field penetrates the sample completely. We will consider different forms for the stochastic perturbations of the high-k limit Ginzburg-Landau model and illustrate, through numerical experiments, their effect on the dynamics of vortices.