There are Asymmetric Minimizers for the One-Dimensional Ginzburg-Landau Model of Superconductivity

S. P. Hastings; W. C. Troy

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There are Asymmetric Minimizers for the One-Dimensional Ginzburg-Landau Model of Superconductivity

S. P. Hastings·W. C. Troy

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Abstract

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 {\it asymmetric} solutions, and only trivial {\it symmetric} solutions. We then 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.

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S. P. Hastings, W. C. Troy. 1999-03-16. There are Asymmetric Minimizers for the One-Dimensional Ginzburg-Landau Model of Superconductivity. https://arxiv.org/abs/cond-mat/9903253

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