In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involv
ing a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.
We present an extensive numerical study of dynamical heterogeneities and their influence on diffusion in an athermal mesoscopic model for actively deformed amorphous solids. At low strain rates the stress dynamics are governed by cooperative regions
of plastic events. On the basis of scaling arguments as well as an extensive numerical study of an athermal elasto-plastic model, we show that there is a direct link between the self-diffusion coefficient and the size of cooperative regions at low strain rates. Both depend strongly on rate and on system size. A measure of the mean square displacement of passive tracers in deformed amorphous media thus gives information about the microscopic rheology, such as the geometry of the cooperative regions and their scaling with strain rate and system size.
