By using the propagator of linear potential as a main tool, we extend the Airy gas (AG) model, originally developed for the three-dimensional (d = 3) edge electron gas, to systems in reduced dimensions (d = 2, 1). First, we derive explicit expressions for the edge particle density and the corresponding kinetic energy density (KED) of the AG model in all dimensions. The densities are shown to obey the local virial theorem. We obtain a functional relationship between the positive KED and the particle density and its gradients and analyze the results inside the bulk as a limit of the local-density approximation. We show that in this limit the KED functional reduces to that of the Thomas–Fermi model in d dimensions.

通过使用线性势传播器作为主要工具，我们将最初为三维 ( d = 3) 边缘电子气开发的艾里气体 (AG) 模型扩展到降维 ( d = 2, 1) 的系统. 首先，我们推导出边缘粒子密度和相应的 AG 模型在所有维度上的动能密度 (KED) 的显式表达式。密度符合局部维里定理。我们获得了正 KED 与粒子密度及其梯度之间的函数关系，并将体内部的结果分析为局部密度近似的极限。我们表明，在这个限制中，KED 泛函在d维上减少到 Thomas-Fermi 模型的泛函。