Deconstructing dynamics of symmetry breaking
The Kibble–Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant $\hat{t}$ when the order parameter catches up with the posttransition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well, we analyze the Landau–Ginzburg model and show why temporal evolution of the order parameter plays such a key role. In conclusion, the analytical solutions we obtain suggest experimentally accessible observables that can shed light on symmetry-breaking dynamics while testing the conjecture on which the KZM is based.