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

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.

24 pages

References in corpus (3)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The BCS functional of superconductivity and its mathematical properties

Cited by in corpus (5)

• Persistence of translational symmetry in the BCS model with radial pair interaction
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• A lower bound for the BCS functional with boundary conditions at infinity
• Condensation of fermion pairs in a domain