Séminaire Maths-Physique

Occupation Density of a Fermi Gas in the Random Phase Approximation

by Sascha Lill (Università degli Studi di Milano)




We consider a 3d fermionic quantum gas at high density in the mean-field regime. For this model, a recent work by Benedikter, Nam, Porta, Schlein and Seiringer introduced a particularly convenient trial state, which is energetically close to the ground state. Within this trial state, we prove a formula for the occupation densities of the momentum space modes. As expected, they converge towards a Fermi ball profile at vanishing coupling, while for low coupling, the Fermi surface persists. Further, our leading-order correction to the Fermi ball profile agrees with the formulas predicted by Daniel and Vosko in 1960. The talk is based on joint work with Niels Benedikter.