  Motivated by experiments in Munich (M. Schreiber et. al. Science
\textbf{349}, 842), we study the dynamics of interacting fermions initially
prepared in charge density wave states in one-dimensional bichromatic optical
lattices. The experiment sees a marked lack of thermalization, which has been
taken as evidence for an interacting generalization of Anderson localization,
dubbed "many-body localization". We model the experiments using an interacting
Aubry-Andre model and develop a computationally efficient low-density cluster
expansion to calculate the even-odd density imbalance as a function of
interaction strength and potential strength. Our calculations agree with the
experimental results and shed light on the phenomena. We also explore a
two-dimensional generalization. The cluster expansion method we develop should
have broad applicability to similar problems in non-equilibrium quantum
physics.
