Harmonically trapped jellium

TL;DR

This paper analyzes a harmonically trapped electron gas model, comparing its energies to uniform electron gases, and finds that in the thermodynamic limit, it behaves like a standard Fermi gas across dimensions.

Contribution

It provides a detailed comparison of kinetic and exchange energies in a confined harmonic potential with uniform electron gas models, extending understanding to finite and infinite systems.

Findings

In the thermodynamic limit, the model's properties match those of a D-dimensional Fermi gas.

The study compares Thomas-Fermi and Dirac coefficients across different paradigms.

Finite-size effects on energies are characterized and contrasted with uniform models.

Abstract

We discuss the model of a $D$-dimensional confined electron gas in which the particles are trapped by a harmonic potential. In particular, we study the non-interacting kinetic and exchange energies of finite-size inhomogeneous systems, and compare the resulting Thomas-Fermi and Dirac coefficients with various uniform electron gas paradigms. We show that, in the thermodynamic limit, the properties of this model are identical to those of the $D$-dimensional Fermi gas.