I’ll give a short review of the recent theoretical progress to explicitly construct non-thermal steady states in quantum systems such as interacting bosons and spin chains. Moreover, I’ll present the recently introduced hydrodynamic description of such non-thermal steady states that allows to study (ballistic) transport properties of many-body systems and to construct non-equilibrium steady states with persistent energy or spin currents and stronger quantum correlations.

* Jacopo De Nardis, École normale supérieure de Paris