  Motivated by a recent experiment, we study the dynamics of bosons in a
disordered optical lattice, interacting with a variably sized bath of disorder
free atoms. As the number of particles in the bath is increased, there is a
transition between "localized" and "ergodic" behavior, which are characterized
by the long-time behavior of an initial density wave. We model the dynamics
with a stochastic mean field theory, reproducing the central observations of
the experiment. A key conclusion from our study is that particle loss plays an
important role.
