Gradient flow in the Ginzburg-Landau model of superconductivity

Abstract

We present numerical studies of the dynamics of vortices in the Ginzburg-Landau model using equations derived from the gradient flow of the free energy. Our equations are equivalent to the time dependent Ginzburg-Landau equations. We have modeled the dynamics of multiple n-vortex configurations starting far from equilibrium. We find generically that there are two timescales for equilibration: a short timescale related to the formation time for a single n-vortex, and a longer timescale that characterizes vortex-vortex interactions.

Nonequilibrium approach to holographic superconductors using gradient flow

“…When the system contains different species of fields, as in our case, one can consider the possibility that the different types of fields diffuse at different rates. For example, one can recover the time-dependent Schrodinger equations considered in the standard Ginsburg-Landau model [12] by considering the following configuration space metric with the following block structure:…”

“…Gradient flow is a general analogue of the heat equation that describes the path of steepest descent with respect to the free energy or Euclidean action of a system. It has been used in a variety of mathematical and physical contexts including Perelman's proof [10] of Thurston's geometrization conjecture, string theory [11], superconductors [12] and even image processing [13], [14].…”