  Observations of center of mass dynamics offer a straightforward method to
identify strongly interacting quantum phases of atoms placed in optical
lattices. We theoretically study the dynamics of states derived from the
disordered Bose-Hubbard model in a trapping potential. We find that the edge
states in the trap allow center of mass motion even with insulating states in
the center. We identify short and long-time scale mechanisms for edge state
transport in insulating phases. We also argue that the center of mass velocity
can aid in identifying a Bose-glass phase. Our zero temperature results offer
important insights into mechanisms of transport of atoms in trapped optical
lattices while putting bounds on center of mass dynamics expected at non-zero
temperature.
