Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model

TL;DR

This paper investigates the dynamics and interactions of knotted topological solitons called Hopfions in the Faddeev-Skyrme model, demonstrating particle-like behavior, charge conservation during scattering, and stability of certain configurations.

Contribution

It provides new insights into the scattering behavior, charge conservation, and stability of Hopfions within the Faddeev-Skyrme model, linking theoretical predictions with dynamical properties.

Findings

Hopfions behave like particles during scattering

Hopf charge is conserved in interactions

Bound states can form during Hopfion dynamics

Abstract

Several materials, such as ferromagnets, spinor Bose-Einstein condensates, and some topological insulators, are now believed to support knotted structures. One of the most successful base-models having stable knots is the Faddeev-Skyrme model and it is expected to be contained in some of these experimentally relevant models. The taxonomy of knotted topological solitons (Hopfions) of this model is known. In this paper we describe some aspects of the dynamics of Hopfions and show that they do indeed behave like particles: during scattering the Hopf charge is conserved and bound states are formed when the dynamics allows it. We have also investigated the dynamical stability of a pair of Hopfions in stacked or side-by-side configurations, whose theoretical stability has been recently discussed by Ward.