Gradient Flow in the Ginzburg-Landau Model of Superconductivity

TL;DR

This paper investigates vortex dynamics in the Ginzburg-Landau model of superconductivity using gradient flow equations, revealing two distinct time scales for vortex formation and interaction through numerical simulations.

Contribution

It introduces numerical modeling of multi-vortex dynamics far from equilibrium based on gradient flow equations, highlighting two key time scales for vortex behavior.

Findings

Identification of two distinct time scales for vortex equilibration

Numerical modeling of multi-vortex dynamics far from equilibrium

Insights into vortex formation and interaction processes

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. These equations have previously been proposed to describe the dynamics of n-vortices away from equilibrium. We are able to model the dynamics of multiple n-vortex configurations starting far from equilibrium. We find generically that there are two time scales for equilibration: a short time scale related to the formation time for a single n-vortex, and a longer time scale that characterizes vortex-vortex interactions.