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Spatiotemporal scaling of two-dimensional nonequilibrium exciton-polariton systems with weak interactions

We perform a numerical study on the two-dimensional nonequilibrium exciton-polariton systems driven by incoherent pumping based on the stochastic generalized Gross-Pitaevskii equation. We calculate the density fluctuation, coherence function, and scaling function. It is found that the correlations at short range agree with the Bogoliubov linear theory. While at large distance, both static and dynamic correlations are characterized by the nonlinear scaling behaviors of Kardar-Parisi-Zhang (KPZ) universality class, especially when the interaction is weak. In this regime, scaling analyses are crucial to capture the universal KPZ scaling features. In addition, the interaction between vortices is modified in the strong KPZ regime and leads to complex nonequilibrium vortex patterns.