The Gell-Mann-Brueckner formula for the correlation energy of the electron gas: a rigorous upper bound in the mean-field regime

DOI10.1007/s00220-023-04672-2zbMath1527.81121arXiv2208.01581MaRDI QIDQ6165433

Christian Hainzl, Martin Ravn Christiansen, Phan Thành Nam

Publication date: 4 July 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.01581

Mathematics Subject Classification ID

Measures of association (correlation, canonical correlation, etc.) (62H20) Electromagnetic interaction; quantum electrodynamics (81V10) Fermionic systems in quantum theory (81V74) Bosonic systems in quantum theory (81V73) PDEs in connection with mean field game theory (35Q89)

Related Items

The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime ⋮ Correlation energy of a weakly interacting Fermi gas with large interaction potential ⋮ Hilbert-Schmidt estimates for fermionic 2-body operators ⋮ On the effective quasi-bosonic Hamiltonian of the electron gas: collective excitations and plasmon modes

Cites Work

• Unnamed Item
• Error bound for the Hartree-Fock energy of atoms and molecules
• Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
• Correlation energy of a weakly interacting Fermi gas
• On the effective quasi-bosonic Hamiltonian of the electron gas: collective excitations and plasmon modes
• Bosonization of fermionic many-body dynamics
• On the correlation energy of interacting fermionic systems in the mean-field regime
• On the energy of a large atom
• Correlation Energy of an Electron Gas at High Density: Plasma Oscillations
• A CORRELATION ESTIMATE WITH APPLICATIONS TO QUANTUM SYSTEMS WITH COULOMB INTERACTIONS
• A Collective Description of Electron Interactions. I. Magnetic Interactions
• A Collective Description of Electron Interactions: II. Collective<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>vs</mml:mi></mml:math>Individual Particle Aspects of the Interactions
• A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas
• A Collective Description of Electron Interactions: IV. Electron Interaction in Metals
• Correlation Energy of an Electron Gas at High Density
• Correlation Energy of an Electron Gas at High Density