Time reparametrization group and the long time behavior in quantum glassy systems

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group (R(rho)G) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out or equilibrium fluctuation-dissipation relation.