论文标题
通风气模型：从三个到减小的尺寸
Airy gas model: From three to reduced dimensions
论文作者
论文摘要
通过使用线性电位的传播器作为主要工具，我们扩展了最初是为三维（$ d = 3 $）的Edge电子气体开发的通风型模型，以减小尺寸的系统（$ d = 2,1 $）。首先，我们在所有维度上的边缘颗粒密度和相应的动能密度（KED）中得出明确的表达式。这些密度显示出遵守局部病毒定理。我们获得正ked和粒子密度及其梯度之间的功能关系，并分析整体内部的结果，以局部密度近似的极限。我们表明，在此限制下，KED功能可将功能减少到$ d $ dimensions中的Thomas-Fermi模型。
By using the propagator of linear potential as a main tool, we extend the Airy gas 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 Airy gas 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.
