Whether a small quantum mechanical system is able to equilibrate with its environment once an external local perturbation drives it out of thermal equilibrium is a central question which cuts across many different fields of science. Here we consider such a problem for a correlated quantum impurity coupled to a fermionic reservoir and driven out of equilibrium by local quantum quenches such as those recently realized in optical absorption experiments on single quantum dots. We argue that

more »

... ation in this problem is deeply connected to the occurrence of Kondo Effect at low energy and that a highly non trivial dynamical behavior may emerge whenever a local quantum critical point intrudes between a conventional Kondo screened phase and a Kondo unscreened one. We discuss this issue in the context of the Anderson Impurity model coupled to a pseudo-gap reservoir by using a correlated time dependent variational wave function that is able to qualitatively describe this physics.