Dynamics and correlations at a quantum phase transition beyond Kibble-Zurek

Kibble-Zurek theory (KZ) stands out as the most robust of defect generation in dynamics phase transitions. KZ utilizes structure equilibrium states away from transition point to estimate excitations due using adiabatic and impulse approximations. Here we show, actual nonequilibrium lead a qualitatively different scenario KZ, far correlations between defects (rather than their densities) are concerned. For quantum Ising chain, this gives rise Gaussian spatial decay domain wall (kinks) correlations, while would predict an exponential fall. We propose simple but general framework on top based ``quantum coarsening'' local correlators supposed regime. outline how our picture extends generic interacting situations.