Desde Abril 11, 2018 16:45 hasta Abril 11, 2018 17:45
On the 3D Ginzburg-Landau model of superconductivity
Abstract:
The ginzburg-landau model is a phenomenological description of superconductivity. A crucial feature is the presence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical field. we are interested in the regime of small ε, where ε>0 is the inverse of the ginzburg-landau parameter (a material constant). In this regime, the vortices are at main order codimension 2 topological singularities.
In this talk i will present a quantitative 3d vortex approximation construction for the ginzburg-landau energy, which provides 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 ε-level. I will then apply these results to describe the behavior of global minimizers for the 3d ginzburg-landau functional below and near the first critical field. I will also provide an ε-quantitative product-type lower bound for the study of ginzburg-landau dynamics.