Faddeev-Hopf knots: Dynamics of linked un-knots
Abstract
We have studied numerically Faddeev-Hopf knots, which are defined as those unit-vector fields in R3 that have a nontrivial Hopf charge and minimize Faddeev's Lagrangian. A given initial configuration was allowed to relax into a (local) minimum using the first order dissipative dynamics corresponding to the steepest descent method. A linked combination of two un-knots was seen to relax into different minimum energy configurations depending on their charges and their relative handedness and direction. In order to visualize the results we plot certain gauge-invariant iso-surfaces.
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