Universality in the dynamics of second-order phase transitions

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogenous and non-homogenous settings. The general nature and extensions of this approach is discussed.