Correlation energy of a weakly interacting Fermi gas

Benedikter, Niels; Nam, Phan Thanh; Porta, Marcello; Schlein, Benjamin und Seiringer, Robert (2021): Correlation energy of a weakly interacting Fermi gas. In: Inventiones Mathematicae, Bd. 225, Nr. 3: S. 885-979

Abstract

We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0020-9910
• Sprache: Englisch