Unwinding in Hopfion vortex bunches

TL;DR

This paper studies the behavior of parallel Faddeev-Hopf vortices under energy minimization, revealing how boundary conditions influence their topological classification and resulting configurations, including intertwined vortex bunches or unwinding.

Contribution

It introduces a new perspective on vortex classification using Pontrjagin invariants and analyzes how boundary conditions affect vortex configurations in the Faddeev-Hopf model.

Findings

Vortices can form intertwined bunches or unwind based on boundary conditions.

Pontrjagin invariants replace Hopf invariant for classification.

Boundary conditions critically influence vortex topology.

Abstract

We investigate the behaviour of parallel Faddeev-Hopf vortices under energy minimization in a system with physically relevant, but unusual boundary conditions. The homotopy classification is no longer provided by the Hopf invariant, but rather by the set of integer homotopy invariants proposed by Pontrjagin. The nature of these invariants depends on the boundary conditions. A set of tightly wound parallel vortices of the usual Hopfion structure is observed to form a bunch of intertwined vortices or unwind completely, depending on the boundary conditions.