Momentum distribution of a Fermi gas with Coulomb interaction in Random Phase approximation

Mathphys Analysis Seminar

I will talk about the momentum distribution of an interacting Fermi gas on a
three dimensional torus in mean field regime in a trial state that reproduces
the Gell-Mann-Brueckner prediction for the correlation energy for Coulomb potential. We show that the momentum distribution is a step function corrected
by the random phase approximation as predicted by Bohm-Pines for a class
of potentials including the Coulomb potential. The key tool for deriving the
distribution is a rigorous bosonization method. The expression for the momentum distribution contains the contributions of collective excitations above the
Fermi-surface going beyond the precision of Hartree-Fock theory. This improves
the result by Benedikter-Lill by being valid a larger class of potentials and for
momenta closer to the Fermi surface.
References
[BL24] Niels Benedikter and Sascha Lill. Momentum distribution of a fermi gas in
the random phase approximation, 202