Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

TL;DR

This paper analyzes vortex interactions in the vector complex Ginzburg--Landau equation, revealing long-range defect interactions and identifying stable rotating bound states called 'vortex molecules' in specific parameter regimes.

Contribution

It provides analytical insights into vortex interactions in CVGLE and discovers stable vortex molecules, a novel bound state configuration.

Findings

Long-range interaction between defects in different fields.

Exponential decay of interaction within the same field.

Existence of stable rotating vortex molecules.

Abstract

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".