On the 3D Ginzburg-Landau model of superconductivity

Abstract: The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the occurrence 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 ɛ, where ɛ>0 is the inverse of the Ginzburg-Landau parameter. 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 functional, 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 ɛ-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 a quantitative product-type estimate for the study of Ginzburg-Landau dynamics.

Date: Apr 02, 2018 at 17:00 h
Venue: Sala de Seminarios Felipe Álvarez Daziano, Depto. de Ingeniería Matemática, 5to piso, Torre Norte, Beauchef 851.
Speaker: Carlos Román
Affiliation: Leipzig University & Max Planck Institute for Mathematics in the Sciences, Germany
Coordinator: Prof. Fethi Mahmoudi
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Posted on May 17, 2018 in CAPDE, Seminars