Equality of the Jellium and the Uniform Electron Gas Energies

Mihály A. Csirik

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arXiv · 2610.20910

Equality of the Jellium and the Uniform Electron Gas Energies

Mihály A. Csirik

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Abstract

Jellium, a system of electrons in a uniform neutralizing background, and the uniform electron gas (UEG), a system of electrons with constant density and no background, are two standard models of the electron gas. We prove that the ground-state energy per unit volume of Jellium, as defined by Lieb and Narnhofer, coincides with the UEG energy defined by Lewin, Lieb and Seiringer, i.e. \[ e^\hbar_{\rm Jel}(ρ_0)=e^\hbar_{\rm UEG}(ρ_0). \] This equality was previously established in the classical case by Lewin, Lieb and Seiringer and independently by Cotar and Petrache.

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Mihály A. Csirik. 2026-10-14. Equality of the Jellium and the Uniform Electron Gas Energies. https://arxiv.org/abs/2610.20910

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