Irreducible Ginzburg-Landau fields in dimension 2

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2018-01-18

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Abstract

Ginzburg--Landau fields are the solutions of the Ginzburg--Landau equations which depend on two positive parameters, $\alpha$ and $\beta$. We give conditions on $\alpha$ and $\beta$ for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in $\rl^2$, spheres, tori, etc.) with de Gennes--Neumann boundary conditions. We also prove that, for each such manifold and all positive $\alpha$ and $\beta$, 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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10.1007/s12220-017-9890-4

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Nagy, Á (2018). Irreducible Ginzburg-Landau fields in dimension 2. 10.1007/s12220-017-9890-4 Retrieved from https://hdl.handle.net/10161/16003.

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