Harmonically trapped jellium
Pierre-Fran\c{c}ois Loos, Peter M. W. Gill

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 -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 -dimensional Fermi gas.
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