  The universal critical behavior of the driven-dissipative non-equilibrium
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 non-equilibrium dynamics, and generalizes Model A for
classical relaxational dynamics with non-conserved 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 non-trivial order
in the dimensional epsilon expansion about the upper critical dimension d_c =
4, and establish the emergence of a novel universal scaling exponent associated
with the non-equilibrium drive. We also discuss the corresponding situation for
a conserved order parameter field, i.e., (sub-)diffusive Model B with complex
coefficients.
