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Faddeev-Hopf knots: Dynamics of linked un-knots

Jarmo Hietarinta·Petri Salo
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Abstract

We have studied numerically Faddeev-Hopf knots, which are defined as those unit-vector fields in $R^3$ 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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Jarmo Hietarinta, Petri Salo. 1998-11-05. Faddeev-Hopf knots: Dynamics of linked un-knots. https://doi.org/10.1016/s0370-2693(99)00054-4

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