3D vortex approximation construction and $\epsilon$-level estimates for the Ginzburg-Landau functional

Abstract

We provide a quantitative three-dimensional vortex approximation construction for the Ginzburg-Landau functional. This construction gives an approximation of vortex lines coupled to a lower bound for the energy, optimal to leading order, analogous to the 2D ones, and valid for the first time at the $\epsilon$-level. These tools allow for a new approach to analyze the behavior of global minimizers for the Ginzburg-Landau functional below and near the first critical field in 3D, followed in two forthcoming papers. In addition, they allow to obtain an $\epsilon$-quantitative product estimate for the study of Ginzburg-Landau dynamics.

73 pages

References in corpus (1)

• Vortex density models for superconductivity and superfluidity

Cited by in corpus (4)

• On the first critical field in the 3D Ginzburg-Landau model of superconductivity
• Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem
• Positive-density ground states of the Gross-Pitaevskii equation
• Wrinkling of an elastic sheet floating on a liquid sphere