Critical dynamics of symmetry breaking: Quenches, dissipation, and cosmology

Symmetry-breaking phase transitions may leave behind topological defects with a density dependence on the quench rate. We investigate the dynamics of such quenches for the one-dimensional, Landau-Ginzburg case and show that the density of kinks, n, scales differently with the quench time scale, tau(Q), depending on whether the dynamics in the vicinity of the critical point is overdamped (n proportional to tau(Q)(-1/4)) or underdamped (n proportional to tau(Q)(-1/3)). Either of these cases may be relevant to the early Universe, and we derive bounds on the initial density of topological defects in cosmological phase transitions. [S0556-2821(98)01820-7].