The dilute Fermi gas via Bogoliubov theory
Tuesday, 10 November, 2020
We consider N spin 1/2 fermions interacting with a positive and regular enough potential in three dimensions. We compute the ground state energy of the system in the dilute regime at second order in the particle density. We recover a well-know expression for the ground state energy which depends on the interaction potentials only via its scattering length. A first proof of this result has been given by Lieb, Seiringer and Solovej. We discuss a new derivation of this formula which makes use of the almost-bosonic nature of the low-energy excitations of the systems. Based on a joint work with Marco Falconi, Christian Hainzl, Marcello Porta.
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