Kinetics of many-body reservoir engineering

Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can be used to understand both the transient and long-time dynamics of many particles coupled to an engineered reservoir in a number-conserving way. For the example of a bosonic array, we show that the nonequilibrium steady state can be expressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with an energy-dependent temperature.