  We investigate the development of winding number and Chern-Simons number in a
tachyonic transition in the SU(2) Higgs model, motivated by the scenario of
cold electroweak baryogenesis. We find that localized configurations with
approximately half-integer winding number, dubbed half-knots, play an important
role in this process. When the Chern-Simons number adjusts locally to the
winding number, the half-knots can stabilize and acquire half-integer
Chern-Simons number as well. We present two examples from numerical
simulations: one half-knot that stabilizes early and one that gives rise to a
late sphaleron transition. We also study the winding number distribution after
the transition and present new results on the development of the Chern-Simons
susceptibility.
