Topological thermalization via vortex formation in ultra-fast quenches

We investigate the thermalization of a two-component scalar field across a second-order phase transition under extremely fast quenches. We find that vortices start developing once the thermal bath sets the control parameter to its final value in the nonsymmetric phase. Specifically, we find that vortices emerge as the fluctuating field relaxes and departs macroscopically from its symmetric configuration. The density of primordial vortices at the relaxation time is a decreasing function of the final temperature of the quench. Subsequently, vortices and antivortices annihilate at a rate that eventually determines the total thermalization time. This rate decreases if the theory contains a discrete anisotropy term, which otherwise leaves the primordial vortex density unaffected. Our results thus establish a link between the topological processes involved in the vortex dynamics and the delay in the thermalization of the system.