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Equality of the Jellium and the Uniform Electron Gas Energies

Primarily AI-generated textHuman understanding: all partsmath-ph — Mathematical Physicsquant-ph — Quantum Physics

Contributed by Mihaly A. Csirik ↗

Version 1 / Oct 29, 2026/ arXiv: 2603.21200 / CC BY 4.0

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. eJelℏ(ρ0)=eUEGℏ(ρ0)e^\hbar_{\rm Jel}(\rho_0)=e^\hbar_{\rm UEG}(\rho_0). This equality was previously established in the classical case by Lewin, Lieb and Seiringer and independently by Cotar and Petrache.

Provenance statement

Lean formalization may be found here: https://github.com/xyzw/jellium_ueg

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Version history

  1. v1Submitted by Mihaly A. CsirikInitial depositCurrentOct 28, 2026