Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs

Rubinstein, Jacob; Schatzman, Michelle

doi:10.1090/S0002-9947-01-02804-5

Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs
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by Jacob Rubinstein and Michelle Schatzman

Trans. Amer. Math. Soc. 353 (2001), 4173-4187

DOI: https://doi.org/10.1090/S0002-9947-01-02804-5

Published electronically: May 17, 2001

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Abstract:

We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.

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