AI 中文总结
本文提出三维极化激元晶体作为观测三维 KPZ 普适类的平台，通过数值模拟证实其满足 KPZ 标度，为研究高维非平衡普适类提供了可控量子流体路径。
AI 中文摘要
Kardar–Parisi–Zhang（KPZ）普适类是微观细致平衡破缺产生宏观标度的实例，此前已在驱动型凝聚体和生长界面中探究了一维、二维实现，但在三维空间维度中展示 KPZ 标度仍是重大挑战。本文提出三维激子-极化激元晶体作为观测三维 KPZ 普适类的平台，从三维光子晶体下极化激元带形成的凝聚体的随机驱动耗散 Gross-Pitaevskii 方程出发，消除大量密度和储库模式，得到凝聚体相位的有效 3+1 维 KPZ 方程。对 KPZ 方程和完整驱动耗散极化激元模型的数值模拟显示，存在中间渐近区域，其中一阶相干性满足 $-\ln |g^{(1)}(0,\Delta t)|\propto |\Delta t|^{2\beta}$ 和 $-\ln |g^{(1)}(\Delta r,0)|\propto |\Delta r|^{2\chi}$，指数与 3+1 KPZ 基准 $\beta=0.1845$、$\chi=0.3135$ 一致。研究确定三维极化激元晶体是通往高维非平衡普适类的可控量子流体路径。
英文摘要
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 $-\ln |\gone(0,Δt)|\propto |Δt|^{2β}$ and $-\ln |\gone(Δr,0)|\propto |Δr|^{2χ}$, 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.
