Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit

TL;DR

This paper demonstrates that in the low-density limit, a fermionic system with specific interactions forms a Bose-Einstein condensate of pairs, which can be described by the Gross-Pitaevskii functional.

Contribution

It establishes a rigorous link between the Bogolubov-Hartree-Fock model for fermions and the Gross-Pitaevskii description of paired condensates in the low-density regime.

Findings

Ground state forms a Bose-Einstein condensate of fermion pairs

The condensate is described by the Gross-Pitaevskii functional

System stability requires specific interaction potential conditions

Abstract

We consider the Bogolubov-Hartree-Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose-Einstein condensate of fermion pairs. The latter can be described by means of the Gross-Pitaevskii energy functional.