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

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

2011-08-29

arxiv.org/abs/1108.5551v1

New J. Phys. 14 (2012) 013013

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 11 figures

Scientific paper

10.1088/1367-2630/14/1/013013

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.

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