  We study the effect of quenched disorder on nonequilibrium systems of
interacting particles, specifically, driven diffusive lattice gases with
spatially disordered jump rates. The exact steady-state measure is found for a
class of models evolving by drop-push dynamics, allowing several physical
quantities to be calculated. Dynamical correlations are studied numerically in
one dimension. We conjecture that the relevance of quenched disorder depends
crucially upon the speed of the kinematic waves in the system. Time-dependent
correlation functions, which monitor the dissipation of kinematic waves, behave
as in pure system if the wave speed is non-zero. When the wave speed vanishes,
e.g. for the disordered exclusion process close to half filling, disorder is
strongly relevant and induces separation of phases with different macroscopic
densities. In this case the exponent characterizing the dynamical correlation
function changes.
