Airy gas model: From three to reduced dimensions

By using the propagatorof linear potential as a main tool,we extend theAiry 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 dimensions.