2014/08/31 by Mathieu Lewin, Elliott H. Lieb, Élliott H. Lieb · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Connection (principal bundle) #Constant (computer programming) #Coulomb #Geometry #High-pressure geophysics and materials #Jellium #Materials science #Mathematical physics #Mathematics #Physics #Planck constant #Quantum #Quantum electrodynamics #Quantum mechanics #Range (aeronautics) #Spectroscopy and Quantum Chemical Studies #math-ph #math.MP #physics.chem-ph
paper · pdf · doi:10.1103/physreva.91.022507
published as Physical Review A, 91, 022507 (2015) · Final version to appear in Physical Review A. Compared to the very first version, this one contains an appendix discussing the link with the Jellium problem
arxiv created 2015/02/11 · openalex publication_date 2015/02/11 · arxiv updated 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria et al. [Int. J. Quantum Chem. 112, 1579 (2012)], except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.