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We summarise here some relevant results related to non-equilibrium quantum systems. We characterise quantum phase transitions (QPT) in out-of-equilibrium quantum systems through a novel approach based on geometrical and topological properties of mixed quantum systems. We briefly describe results related to non-perturbative studies of the bistable dynamics of a quantum particle coupled to an environment. Finally, we shortly summarise recent studies on the generation of solitons in current-biased long Josephson junctions.