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.
Correlation energy of a weakly interacting Fermi gas / Benedikter, N.; Nam, P. T.; Porta, M.; Schlein, B.; Seiringer, R.. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - 225:3(2021), pp. 885-979. [10.1007/s00222-021-01041-5]
Correlation energy of a weakly interacting Fermi gas
Benedikter, N.;Porta, M.;Schlein, B.;
2021-01-01
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.File | Dimensione | Formato | |
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