  We analyze the dynamics of an initially trapped cloud of interacting quantum
particles on a lattice under a linear (Stark) potential. We reveal a dichotomy:
initially trapped interacting systems possess features typical of both
many-body-localized and self-thermalizing systems. We consider both fermions
($t$-$V$ model) and bosons (Bose-Hubbard model). For the zero and infinite
interaction limits, both systems are integrable: we provide analytic solutions
in terms of the moments of the initial cloud shape, and clarify how the
recurrent dynamics (many-body Bloch oscillations) depends on the initial state.
Away from the integrable points, we identify and explain the time scale at
which Bloch oscillations decohere.
