Phase equilibration in bubble collisions

In the context of an Abelian gauge symmetry, spontaneously broken at a first-order transition, we discuss the evolution of the phase difference between the Higgs fields in colliding bubbles. We show that the effect of dissipation, represented by a finite plasma conductivity, is to cause the phases to equilibrate on a time scale, determined by the conductivity, which can be much smaller than the bubble radii at the time of collision. Currents induced during the phase equilibration generate a magnetic flux, which is determined by the initial phase difference. In a three-bubble collision, the fluxes produced by each pair of bubbles combine, and a vortex can be formed. We find that, under most conditions, the probability of trapping magnetic flux to form a vortex is correctly given by the ‘‘geodesic rule.’’