Correlation energy of a weakly interacting Fermi gas

In this paper, based on [N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Commun. Math. Phys. 374(3) (2020) 2097–2150; N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas, Invent. Math. 225(3) (2021) 885–979; N. Benedikter, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas with large interaction potential, preprint (2021), arXiv:2106.13185], we present a recent estimate for the correlation energy of a Fermi gas in the so-called mean-field regime and we outline some of the main ideas of its proof.In this paper, based on [N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime, Commun. Math. Phys. 374(3) (2020) 2097–2150; N. Benedikter, P. T. Nam, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas, Invent. Math. 225(3) (2021) 885–979; N. Benedikter, M. Porta, B. Schlein and R. Seiringer, Correlation energy of a weakly interacting Fermi gas with large interaction potential, preprint (2021), arXiv:2106.13185], we present a recent estimate for the correlation energy of a Fermi gas in the so-called mean-field regime and we outline some of the main ideas of its proof.

Reviews in Mathematical PhysicsJun 23, 20230 citations

Energetics of a strongly correlated Fermi gas

Shina Tan

arXiv:cond-mat/0505200Annals of PhysicsMar 27, 2008654 citations

Spin-energy correlation in degenerate weakly interacting Fermi gases

Saeed Pegahan, Jayampathi Kangara, Ilya Arakelyan +1 more

The time evolution of spin-energy correlations in a very weakly interacting Fermi gas of ${}^{6}$ Li produces complex spin-density profiles, which are observed and quantitatively explained by a one-dimensional mean-field model. This system exhibits rich collective dynamics for exploring the interplay between spin, motion, Fermi statistics, and interactions in many-body systems.The time evolution of spin-energy correlations in a very weakly interacting Fermi gas of ${}^{6}$Li produces complex spin-density profiles, which are observed and quantitatively explained by a one-dimensional mean-field model. This system exhibits rich collective dynamics for exploring the interplay between spin, motion, Fermi statistics, and interactions in many-body systems.

arXiv:1812.08832Physical Review AJun 20, 201914 citations

Correlation energy of a weakly interacting Fermi gas

Niels Benedikter, Phan Thành Nam, Marcello Porta +2 more

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.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.

arXiv:2005.08933Inventiones mathematicaeMay 3, 202130 citations

The time evolution of spin-energy correlations in a very weakly interacting Fermi gas of

{}^{6}

Li produces complex spin-density profiles, which are observed and quantitatively explained by a one-dimensional mean-field model. This system exhibits rich collective dynamics for exploring the interplay between spin, motion, Fermi statistics, and interactions in many-body systems.