Equality of the Jellium and the Uniform Electron Gas Energies
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. $e^\hbar_{\rm Jel}(\rho_0)=e^\hbar_{\rm UEG}(\rho_0)$. This equality was previously established in the classical case by Lewin, Lieb and Seiringer and independently by Cotar and Petrache.
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