We consider a time-dependent Ginzburg-Landau equation for superconductors with a strictly complex relaxation parameter, and derive motion laws for the vortices in the case of a finite number of vortices in a bounded magnetic field. The motion laws correspond to the flux-flow Hall effect. As our main tool, we develop a quantitative Γ-stability result relating the Ginzburg-Landau energy to the renormalized energy.
Bibliographical noteFunding Information:
The research presented in this article was begun while the authors enjoyed the hospitality of the Hausdorff Research Institute for Mathematics, Bonn. MK was supported by DFG SFB 611. DS was supported by NSF grant DMS-0707714. The authors wish to thank the anonymous referees for numerous suggestions that significantly improved the presentation of the results.
- Ginzburg-Landau theory
- Vortex dynamics