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arXiv · 1210.6315

Some remarks concerning symmetry-breaking for the Ginzburg-Landau equation

Pierpaolo Esposito
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Abstract

The correlation term, introduced in [13] to describe the interaction between very far apart vortices, governs symmetry-breaking for the Ginzburg-Landau equation in R^2 or bounded domains. It is a homogeneous function of degree (-2), and then for 2π/N-symmetric vortex configurations can be expressed in terms of the so-called correlation coefficient. Ovchinnikov and Sigal [13] have computed it in few cases and conjectured its value to be an integer multiple of π/4. We will disprove this conjecture by showing that the correlation coefficient always vanishes, and will discuss some of its consequences.

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Pierpaolo Esposito. 2012-10-23. Some remarks concerning symmetry-breaking for the Ginzburg-Landau equation. https://arxiv.org/abs/1210.6315

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