Quantum dynamical field theory for nonequilibrium phase transitions in driven open systems

We develop a quantum dynamical field theory for studying phase transitions in driven open systems coupled to Markovian noise, where nonlinear noise effects and fluctuations beyond semiclassical approximations influence the critical behavior. We systematically compare the diagrammatics, the properties of the renormalization group flow, and the structure of the fixed points of the quantum dynamical field theory and of its semiclassical counterpart, which is employed to characterize dynamical criticality in three-dimensional driven-dissipative condensates. As an application, we perform the Keldysh functional renormalization of a one-dimensional driven open Bose gas, where a tailored diffusion Markov noise realizes an analog of quantum criticality for driven-dissipative condensation. We find that the associated nonequilibrium quantum phase transition does not map into the critical behavior of its three-dimensional classical driven counterpart.