Symmetry breaking phase transitions and their dynamics are at the heart of a broad range of physical phenomena ranging from the physics of the early universe to solid state physics. Of particular interest are dynamical properties when traversing such a symmetry-breaking second-order phase transition at a finite rate as then spatially separated parts of the system may chose symmetry-broken phases independently and where such choices are incompatible, topological defects form whose number dependence on the quench rate is given by simple power laws.
Typically these powerlaws are derived by physical arguments which works well in simple cases but can lead to wrong conclusions in complex situations involving for example spatial inhomogeneities. 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 homogeneous and nonhomogeneous settings.