Nonequilibrium phase diagram of a driven and dissipative many-body system

We study the nonequilibrium dynamics of a many-body bosonic system on a lattice, subject to driving and. The time evolution is described by a master equation, which we treat within a generalized Gutzwiller field approximation for density matrices. The dissipative processes are engineered such that the system, the absence of interaction between the bosons, is driven into a homogeneous steady state with off-diagonal -range order. We investigate how the coherent interaction affects the properties of the steady state of the qualitatively and derive a nonequilibrium phase diagram featuring a phase transition into a steady state long-range order. The phase diagram also exhibits an extended domain where an instability of the steady state gives rise to a persistent density pattern with spontaneously broken translational. In the limit of low particle density, we provide a precise analytical description of the time evolution the instability. Moreover, we investigate the transient following a quantum quench of the dissipative and we elucidate the prominent role played by collective topological variables in this regime.