| Summary: | The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (sub)diffusive model B with complex coefficients.
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