Nonequilibrium functional renormalization for driven-dissipative Bose-Einstein condensation

We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. The starting point is a microscopic description of the system in terms of a many-body quantum master equation, where coherent and driven-dissipative dynamics occur on an equal footing. An equivalent Keldysh real-time functional integral reformulation opens up the problem to a practical evaluation using the tools of quantum field theory. In particular, we develop a functional renormalization group approach to quantitatively explore the universality class of this stationary nonequilibrium system. Key results comprise the emergence of an asymptotic thermalization of the distribution function, while manifest nonequilibrium properties are witnessed in the response properties in terms of a new, independent critical exponent. Thus, the driven-dissipative microscopic nature is seen to bear observable consequences on the largest length scales. The absence of two symmetries present in closed equilibrium systems-underlying particle number conservation and detailed balance, respectively-is identified as the root of this new nonequilibrium critical behavior. Our results are relevant for broad ranges of open quantum systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases.