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Superconductivity in mesoscopic domains

  • Michelle Schatzman (Universität Lyon)
A3 01 (Sophus-Lie room)

Abstract

Let M be a graph embedded in the plane. The lace around M is

the open

set Otex2html_wrap_inli
</p>
<p>ne7 of thickness

2tex2html_wrap_inline7

around the edges

of M, and smoothed close to the vertices of M. The details of

the

smoothing will be proved to be irrelevant. The unknowns in the

two-dimensional Ginzburg-Landau functional are the vector potential and

the complex order parameter. As

tex2html_wrap_inline7

tends to 0, it is possible

to extract from any sequence of minimizers a converging subsequence whose

limit is a minimizer of a one-dimensional Ginzburg-Landau functional on

M. The only unknown in this functional is a complex order parameter.

 

A further reduction leads to a new functional depending only on a real

valued function and n integers, n being the number of indepen

dent

cycles of the graph, or equivalently the number of holes in

R2 \ M.

seminar
4/18/24 5/30/24

Oberseminar Analysis

Universität Leipzig Augusteum - A314

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail

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