A convexified energy functional for the Fermi-Amaldi correction
The authors consider a quantum mechanical system of \(N\) electrons in \({\mathbb R}^3\) interacting through Coulomb interaction, with \(N_1\) spin up and \(N_2\) spin down. They study the Thomas-Fermi energy with the Fermi-Amaldi correction. As this functional is not convex, they replace it by a convex minorant \(E\) and they prove that this modified energy has a unique minimizing density provided that \(N_1\) is close to \(N_2\).
scientific article; zbMATH DE number 5725453