Abstract
We study in two dimensions a Ginzburg-Landau equation for a complex amplitude, with broken phase invariance. The addition of non-variational terms breaks the chiral symmetry of the equation and leads to striking effects. A non-variational term is provided by an external, complex field with time dependence. Our results, which are for two dimensional systems, can be phrased in the language of domain walls. We investigate how these walls move when a weak, complex magnetic field, is applied. There occurs spiral type behavior around stationary points, where the amplitude is zero, and there exists a critical radius above which circular domains grow.
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