2026/07/30 by Junhui Cao, Denis Novokreschenov, Artem Alexandrov +2
Physics and Astronomy · #cond-mat.stat-mech
arxiv created 2026/07/30 · arxiv updated 2026/07/31
Kardar--Parisi--Zhang (KPZ) universality provides an example of macroscopic scaling generated by microscopic violation of detailed balance. While one- and two-dimensional realizations have been explored in driven condensates and growing interfaces, demonstrating KPZ scaling in three spatial dimensions remains a major challenge. Here we propose a three-dimensional exciton-polariton crystal as a platform for observation of 3D KPZ universality. Starting from a stochastic driven-dissipative Gross-Pitaevskii equation for a condensate formed in a three-dimensional photonic-crystal lower-polariton band, we eliminate the massive density and reservoir modes and obtain an effective 3+1-dimensional KPZ equation for the condensate phase. Numerical simulations of both the KPZ equation and the full driven-dissipative polariton model show an intermediate-asymptotic regime in which the first-order coherence obeys -ln |\gone(0,Δt)|∝ |Δt|2β and -ln |\gone(Δr,0)|∝ |Δr|2χ, with exponents consistent with the 3+1 KPZ benchmarks β= 0.1845, χ= 0.3135. Our results identify three-dimensional polariton crystals as a controllable quantum fluid route to higher-dimensional nonequilibrium universality.