Airy gas model: From three to reduced dimensions

Abstract

We derive explicit expressions for the edge particle density and the corresponding kinetic energy density (KED) of the Airy gas model in d dimensions (d=1,2,3). 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 in d dimensions. We 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.