Driven dynamics of glassy systems: From spin glasses to complex fluids

We present a theoretical study of the off-equilibrium dynamics of a large class of microscopic systems, whose common feature is to present, under specific experimental conditions, an extremely slow (`glassy') relaxation. We first tackle the question of aging in glassy systems, developing a quantitative comparison between two theoretical descriptions, namely (i) domain growth processes, (ii) analytical solution of mean-field disordered spin models. We next study the case where the dynamics is driven by an external force. This situation is important for applications (rheology of supercooled liquids and complex fluids, slow compaction of granular materials, etc.), and its systematic investigation is an original aspect of this work. In this context, we first numerically study the effect of a flow on the phase separation of a binary mixture. The (Temperature, Drive) phase diagram of structural and spin glasses is then investigated in the mean-field approximation. We consider the two cases of a constant, nonconservative and then conservative but time-dependent, driving force. These studies result in a microscopic -shape of the relaxation, effective temperature defined via the fluctuation-dissipation theorem-, and macroscopic -flow curves, dynamic phase transition- description. The main results are numerically tested on realistic models for supercooled liquids and spin glasses.