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

Many-body quantum dynamics of initially trapped systems due to a Stark potential --- thermalization vs. Bloch oscillations