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 second order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic field. We show that for an appropriate range of parameters there are asymmetric solutions, and only trivial symmetric solutions. We then correct an error of the authors in [9] and show that the associated energy function is negative for the asymmetric solutions, and zero for the trivial symmetric solution. It follows that a global minimizer of the energy is asymmetric. This property resolves a conjecture of Marcus [13].