Disorder, synchronization and phase locking in non-equilibrium Bose-Einstein condensates

We review some theories of non-equilibrium Bose-Einstein condensates in potentials, in particular of the Bose-Einstein condensate of polaritons. We discuss such condensates, which are steady-states established through a balance of gain and loss, in the complementary limits of a double-well potential and a random disorder potential. For equilibrium condensates, the former corresponds to a Josephson junction, whereas the latter is the setting for the superfluid/Bose glass transition. We explore the non-equilibrium generalization of these phenomena, and highlight connections with mode selection and synchronization.