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Dynamics of Hopfions

Wednesday 5th December 2012 - 14:10 to 14:30
INI Seminar Room 1
Session Title: 
Knots in mathematics: Knot energies
Session Chair: 
Clayton Shonkwiler
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 talk, we describe the basic properties of static Hopfions, known for quite a long time before discussing some aspects of the dynamics of Hopfions, how the static properties survive in the dynamical situation, 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons