KPZ Physics in Exciton Polaritons Systems
Davide Squizzato (LPMMC, Grenoble)
The experimental demonstration of Bose-Einstein condensation of exciton polaritons gases in driven-dissipative conditions  has given rise to several questions on the nature and the characterization of out-of-equilibrium bosonic systems under pump and dissipation. Such systems can be theoretically described by a generalised Gross-Pitaevskii equation (gGPE) in which complex coefficients and noise enrich the equilibrium picture. An analytical mapping between gGPE and the Kardar-Parisi-Zhang (KPZ) equation has been demonstrated at long wavelength if fluctuations of the amplitude of the condensate are negligible with respect to the ones of the phase field. Hence, one expects the long-distance properties of driven-dissipative condensates to pertain to the KPZ universality class. A numerical verification of KPZ scaling was given in (1+1)dimensions ; however, the experimental accessibility of the KPZ mapping is still under debate. In this work we use both Keldysh field-theoretical approach and numerical simulations to investigate the effects of inhomogeneities typical of experimental set-ups and study their effects on the universal properties of driven-dissipative polaritons condensates; we furthermore look at the real-time statistics of the phase in both homogeneous and in-homogeneous case in order to better understand the nature of KPZ behaviour, i.e. the geometrical sub-class to which it belongs to.