Renormalized Energy and Vortex Interaction in Finsler Ginzburg-Landau Models

TL;DR

This paper introduces a Finsler geometric framework for analyzing vortex interactions in anisotropic superconductors, leading to a new renormalized energy model that captures directional dependence and vortex dynamics.

Contribution

It develops a novel Finsler Ginzburg-Landau model, deriving the Gamma-limit and analyzing vortex behavior with anisotropic dissipation and drift.

Findings

Finsler structure encodes anisotropic energy dependence.

Vortex motion follows a Finsler gradient flow.

Established stability and analytical structure of the renormalized energy.

Abstract

We develop a Finsler Ginzburg--Landau framework for the analysis of vortex interactions in anisotropic superconductors. Within this setting, the Finsler structure encodes directional dependence of the condensate energy, yielding a renormalized energy W_F that governs both equilibrium and dynamics of vortices. We derive the Gamma--limit, establish the analytical structure and stability of W_F, and show that vortex motion follows a Finsler gradient flow exhibiting anisotropic dissipation and drift. This approach provides a unified geometric and physical model for anisotropic superconductivity.