Critical Initial Slip Scaling for Driven-dissipative Bose-Einstein Condensation

We investigate the universal non-equilibrium critical behavior at the driven- dissipative Bose-Einstein condensation phase transition by means of the perturbative field-theoretic renormalization group method. Such criticality may be realized experimentally in driven open systems on the interface of quantum optics and many-body physics, ranging from exciton--polariton condensates in optically pumped semiconductor wells to cold atomic gases. We describe the critical dynamics through a noisy and dissipative Gross- Pitaevski or time-dependent Ginzburg-Landau equation with complex coefficients. We focus on the universal critical behavior of this system in the early stages of the relaxation process following a quench from an initially (Gaussian distributed) disordered state that is characterized by broken time translation invariance and governed by the ``initial slip'' exponent $\theta $. We compute $\theta $ to first order in the dimensional $\varepsilon = $ 4 -- d expansion with respect to the upper critical dimension d$=$4, and find that its one-loop value is identical to that of the classical relaxational model A for a two-component non-conserved order parameter.