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arXiv · 1607.00232

Irreducible Ginzburg-Landau fields in dimension 2

Ákos Nagy
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Abstract

Ginzburg-Landau fields are the solutions of the Ginzburg-Landau equations which depend on two positive parameters, $α$ and $β$. We give conditions on $α$ and $β$ for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in $\mathbb{R}^2$, spheres, tori, etc.) with de Gennes-Neumann boundary conditions. We also prove that, for each such manifold and all positive $α$ and $β$, the Ginzburg-Landau free energy is a Palais-Smale function on the space of gauge equivalence classes, Ginzburg-Landau fields exist for only a finite set of energy values, and the moduli space of Ginzburg-Landau fields is compact.

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Ákos Nagy. 2018-11-26. Irreducible Ginzburg-Landau fields in dimension 2. https://doi.org/10.1007/s12220-017-9890-4

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