Superconductivity in mesoscopic domains

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


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

the open

set Otex2html_wrap_inli
<p>ne7 of thickness


around the edges

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


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


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


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

R2 \ M.

4/18/24 5/30/24

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