Expansion in the distance parameter for two vortices close together

TL;DR

This paper investigates the behavior of two closely spaced static vortices in 2D, deriving an expansion for their relative positions and comparing models to Ginzburg-Landau theory, revealing similarities and differences in their angular and radial dependencies.

Contribution

It introduces an expansion method for vortex interactions in a simple complex field model and compares it with Ginzburg-Landau theory, highlighting both common patterns and differences.

Findings

Angular dependence patterns are similar in both models.

Radial functions differ up to third order.

Expansion formulas involve trigonometric and exponential functions.

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.