We investigate the dynamics of collisions of bubbles formed in a first order phase transition in 2+1 dimensions and study the production of vortices. A numerical simulation is carried out by prescribing bubble configurations as part of the initial data and then evolving by equations of motion. We study nonuniformities in the vortex configuration caused by asymmetries in bubble collisions and find that it can lead to large vortex velocities (0.3c–0.6c). We also simulate the vortex production in a phase transition by randomly nucleating bubbles at various time steps and study the distribution of vortices produced. Our results show that initially a relatively large number of vortices form. Some vortex-antivortex pairs annihilate with the final number of vortices being consistent with the usual estimates based on the Kibble mechanism. The average initial velocity of the vortices is found to be ≃0.4c. We have investigated the dynamics of subcritical bubbles which shows many novel features. We find that a collapsing subcritical bubble bounces back after each collapse and can lead to the formation of a vortex if two (or more) critical bubbles collide with it with appropriate values of Higgs phases. This vortex has a large velocity due to the large momentum of the critical bubble walls and eventually escapes into the false vacuum. Our results have implications for cosmic strings as well as for certain condensed matter systems (such as liquid crystals) which may provide a testing ground for these results (when viscosity, etc., are properly accounted for).

• Received 6 November 1991

DOI:https://doi.org/10.1103/PhysRevD.46.1353