Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium behavior is observed, even when the perturbation is very slow. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order quantum transitions, the scaling behavior is universal, and some scaling functions can be exactly computed. For continuous quantum transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our scaling approach is applied to the quantum Ising ring which presents both first-order and continuous quantum transitions.