  We explore the quench dynamics of a two-dimensional, weakly interacting
disordered Bose gas for various relative strengths of interactions and
disorder. This allows us to identify two well distinct out-of-equilibrium
regimes. When interactions are smaller than the disorder, the gas experiences
multiple scattering and exhibits a short-range spatial coherence. At short time
this coherence is only smoothly affected by interactions, via a diffusion
process of the particles' energies. When interactions are larger than the
disorder, scattering ceases and the gas behaves more and more like a fluid,
ultimately like a superfluid at low energy. In the superfluid regime, the gas
exhibits a long-range algebraic coherence, characteristic of a pre-thermal
regime in disorder.
