Expansion in the distance parameter for two vortices close together

Abstract

Static vortices close together are studied for two different models in 2-dimen- sional Euclidean space. In a simple model for one complex field an expansion in the parameters describing the relative position of two vortices can be given in terms of trigonometric and exponential functions. The results are then compared to those of the Ginzburg-Landau theory of a superconductor in a magnetic field at the point between type-I and type-II superconductivity. For the angular dependence a similar pattern emerges in both models. The differences for the radial functions are studied up to third order.