Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs

TL;DR

This paper investigates the low density behavior of a Fermi gas under BCS theory, demonstrating that with bound states, it approximates a Bose-Einstein condensate described by the Gross-Pitaevskii functional.

Contribution

It establishes a rigorous connection between BCS theory at low density and Bose-Einstein condensation of fermion pairs via the Gross-Pitaevskii functional.

Findings

Fermi gas at low density approximates Bose-Einstein condensate

System described by Gross-Pitaevskii functional

Bound states enable this approximation

Abstract

We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.