Space of initial conditions and universality in nonequilibrium quantum dynamics

We study analytically the role of initial conditions in nonequilibrium quantum dynamics considering one-dimensional ferromagnets regime spontaneously broken symmetry. analyze expectation value local operators for infinite-dimensional space domain wall type, generally intended as spatially interpolating between two different ground states. At large times unitary time evolution takes place inside a light cone produced by spatial inhomogeneity condition. In innermost part form space-time dependence is universal, sense that it specified data equilibrium universality class. The global limit shape variable $x/t$ changes with systems more than states tuning an interaction parameter can induce transition which analog interfacial wetting occurring classical at equilibrium. illustrate general results through examples Ising, Potts and Ashkin-Teller chains.