Bogoliubov Theory for the Dilute Fermi Gas in Three Dimensions

Emanuela L. Giacomelli

C. Drischler, Corbinian Wellenhofer, K. Hebeler +1 more

Emanuela L. Giacomelli

In a dilute system of N fermions with spin 1/2 in three dimensions, we study the correlation energy which is given by the difference between the ground state energy and the energy of the non-interacting Fermi sea state. We review some recent results from the paper by Falconi et al. [Ann. Henri Poincaré 22 (2021), 2283-2353], where we make use of the almost-bosonic nature of the low-energy excitations of the system which can be effectively described by Bogoliubov theory.

Christian Brennecke

Marco Falconi, Emanuela L. Giacomelli, Christian Hainzl +1 more

We study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interaction potentials. We recover a well-known expression for the ground state energy at second order in the particle density, which depends on the interaction potential only via its scattering length. The first proof of this result has been given by Lieb, Seiringer and Solovej (Phys Rev A 71:053605, 2005). In this paper, we give a new derivation of this formula, using a different method; it is inspired by Bogoliubov theory, and it makes use of the almost-bosonic nature of the low-energy excitations of the systems. With respect to previous work, our result applies to a more regular class of interaction potentials, but it comes with improved error estimates on the ground state energy asymptotics in the density.