article published yes Niels P Benedikter author 3DE6C32A-F248-11E8-B48F-1D18A9856A870000-0002-1071-6091 Phan Thành Nam author Marcello Porta author Benjamin Schlein author Robert Seiringer author 4AFD0470-F248-11E8-B48F-1D18A9856A870000-0002-6781-0521 RoSe department IST Austria Open Access Fund project Analysis of quantum many-body systems project 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. https://research-explorer.ista.ac.at/download/7901/11386/2021_InventMath_Benedikter.pdf application/pdfno Springer2021 eng 0020-9910 1432-1297 2005.08933 00064657360000110.1007/s00222-021-01041-5 225885-979 Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>, vol. 225, Springer, 2021, pp. 885–979, doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a>. Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.” <i>Inventiones Mathematicae</i>. Springer, 2021. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a>. Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. 2021;225:885-979. doi:<a href="https://doi.org/10.1007/s00222-021-01041-5">10.1007/s00222-021-01041-5</a> N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas,” <i>Inventiones Mathematicae</i>, vol. 225. Springer, pp. 885–979, 2021. Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979. N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones Mathematicae 225 (2021) 885–979. Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2021). Correlation energy of a weakly interacting Fermi gas. <i>Inventiones Mathematicae</i>. Springer. <a href="https://doi.org/10.1007/s00222-021-01041-5">https://doi.org/10.1007/s00222-021-01041-5</a> 79012020-05-28T16:48:20Z2025-04-14T07:27:00Z