Unwinding in Hopfion vortex bunches
arXiv:0904.1305 · doi:10.1103/PhysRevD.79.125027
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.
6 pages, 9 figures, minor clarifications of text and corrected the final energy of the vortices section IV.B. To be published in Phys.Rev.D
References in corpus (9)
- First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
- Knots and Particles
- To be or knot to be?
- Static solitons with non-zero Hopf number
- Topological surface states in three-dimensional magnetic insulators
- Solitons, Links and Knots
- Faddeev-Hopf knots: Dynamics of linked un-knots
- Knots in the Skyrme-Faddeev model
- Relaxation of twisted vortices in the Faddeev-Skyrme model
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