Unwinding in Hopfion vortex bunches

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.