Renormalized Energy and Vortex Interaction in Finsler Ginzburg-Landau Models

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.