Scaling properties of one-dimensional driven-dissipative condensates

TL;DR

This study numerically analyzes a one-dimensional driven-dissipative condensate, demonstrating its scaling behavior aligns with the KPZ universality class and confirming experimental observability in exciton-polariton systems.

Contribution

The paper provides the first numerical verification that the scaling exponents of a driven-dissipative condensate match those of the KPZ equation, linking non-equilibrium condensate dynamics to KPZ universality.

Findings

Scaling exponents match KPZ predictions

Temporal correlator exhibits stretched-exponential decay

Experimental conditions for observing KPZ scaling are identified

Abstract

We numerically investigate the scaling properties of a one-dimensional driven-dissipative condensate described by a stochastic complex Ginzburg-Landau equation (SCGLE). We directly extract the static and dynamical scaling exponents from the dynamics of the condensate's phase field, and find that both coincide with the ones of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation. We furthermore calculate the spatial and the temporal two-point correlation functions of the condensate field itself. The decay of the temporal two-point correlator assumes a stretched-exponential form, providing further quantitative evidence for an effective KPZ description. Moreover, we confirm the observability of this non-equilibrium scaling for typical current experimental setups with exciton-polariton systems, if cavities with a reduced $Q$ factor are used.