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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