## Seminar Analysis and Mathematical Physics: Emanuela Giacomelli (LMU Munich)

**The dilute Fermi gas via Bogoliubov theory**

Abstract:

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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