Airy gas model: from three to reduced dimensions

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.

Automated summary

By utilizing the propagator of linear potential, the Airy gas model originally developed for three-dimensional edge electron gas is extended to systems with reduced dimensions. Explicit expressions for edge particle density and corresponding kinetic energy density in all dimensions are derived, which adhere to the local virial theorem. A functional relationship between positive KED and particle density with gradients is established, with the KED functional reducing to that of the Thomas-Fermi model in d dimensions in the limit of local-density approximation.