THERE ARE ASYMMETRIC MINIMIZERS FOR THE ONE-DIMENSIONAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY

We study a boundary value problem associated with a system of two seco nd-order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic fie ld. We show that for an appropriate range of parameters there are asym metric solutions and only trivial symmetric solutions. We then correct an error of the authors in [Nonlinear Problems in Applied Mathematics , SIAM, Philadelphia, PA, 1996, pp. 150-158] and show that the associa ted energy function is negative for the asymmetric solutions. Since th e energy is zero for the trivial symmetric solution, it follows that a global minimizer of the energy is asymmetric. This property resolves a conjecture of Marcus [Rev. Mod. Phys., 36 (1964), pp. 294{299].