Open many-body quantum systems have recently gained renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. A series of results in diverse setups is presented, based on a Master equation approach to describe the dissipative dynamics of ultracold bosons in a one-dimensional lattice. The creation of mesoscopic stable many-body structures in the lattice is predicted and the non-equilibrium transport of neutral atoms in the regime of strong and weak interactions is studied.
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