Functional Renormalization for pinned elastic systems away from their steady states

Using one loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits non trivial two-time dynamical regimes with exponents and scaling functions obtained in a dimensional expansion. The aging and equilibrium dynamics of the super-rough glass phase of the random Sine-Gordon model at low temperature is found to be characterized by a single dynamical exponent $z \approx c/T$, where $c$ compares well with recent numerical work. This agrees with the thermal boundary layer picture of pinned systems.