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 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 recently been discussed by Ward.
Highlights
1.1 BackgroundTopological solitons play an important role in many areas of physics
Knot deformations correspond to ribbon deformations, which allow certain types of crossing and breaking, in which the Hopf charge will be conserved
For the same speeds but with slightly smaller impact parameter value 3.6 the result is entirely different (Figure 6, Movie S5). For a moment it seems that the Hopfions would again continue along their individual trajectories but there is just enough time to form an elongated loop. After this the evolution is typical for the total charge |Q| = 6 case: The loop behaves like an over-twisted rubber band and proceeds to make one ribbon crossing deformation to reach the linked loop configuration that is standard for this Hopf charge
Summary
Topological solitons play an important role in many areas of physics. Knotted structures have a long history in physics They were first considered by Lord Kelvin, who proposed in 1867 [11] that atoms could be knotted tubes of ether. This idea did not yield a satisfactory atomic theory, but subsequently more realistic models have been proposed with potential for knotted structures. This has been done, for example, in the context of ferromagnets[12], Bose-Einstein condensates[13], and optics[14]. A unifying feature of all these, in addition to the knotted structures, is that all these phenomena and their knots can be described by classical field theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
