Affiliation: | Department of Mathematics, Technion, Haifa 32000, Israel ; UMR 5585 CNRS MAPLY, Laboratoire de Mathématiques Appliquées de Lyon, Université Claude Bernard -- Lyon 1, 69622 Villeurbanne Cedex, France |
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. |