Vortex dynamics of the full time‐dependent Ginzburg‐Landau equations

Abstract

Abstract In the Ginzburg‐Landau model for superconductivity a large Ginzburg‐Landau parameter κ corresponds to the formation of tight, stable vortices. These vortices are located exactly where an applied magnetic field pierces the superconducting bulk, and each vortex induces a quantized supercurrent about the vortex. The energy of large‐κ solutions blows up near each vortex which brings about difficulties in analysis. Rigorous asymptotic static theory has previously established the existence of a finite number of the vortices, and these vortices are located precisely at the critical points of the renormalized energy (the free energy less the vortex self‐induction energy). A rigorous study of the full time‐dependent Ginzburg‐Landau equations under the classical Lorentz gauge is done under the asymptotic limit κ → ∞. Under slow times the vortices remain pinned to their initial configuration. Under a fast time of order κ the vortices move according to a steepest descent of the renormalized energy. © 2002 John Wiley & Sons, Inc.