Superfluid-insulator transition in a moving system of interacting bosons Anatoli Polkovnikov Harvard University Cold atomic systems with their high tunability and nearly perfect isolation from environment became very attractive for studying strongly correlated systems. Particularly exciting is the possibility to address problems of quantum dynamics far from equilibrium, which are beyond the reach of conventional condensed matter systems. Most of theoretical studies of dynamics in these systems employ essentially classical (Gross-Pitaevskii) equations of motion. At the same time in equilibrium a lot is known about various quantum regimes, where the classical description does not work. In this talk I will discuss a problem where both quantum and dynamic effects are important. In particular, I will describe a moving system of interacting bosons in a periodic optical lattice potential and generalize the conventional superfluid-Mott insulator transition to this highly non-equilibrium situation. I will discuss implications of our results to recent and future experiments.