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

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.

LaTeX2e, 17 pages

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Weakly bound dimers of fermionic atoms
• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The BCS Critical Temperature for Potentials with Negative Scattering Length

Cited by in corpus (12)

• Mean-field Evolution of Fermionic Systems
• The BCS functional of superconductivity and its mathematical properties
• Incompatibility of time-dependent Bogoliubov--de-Gennes and Ginzburg--Landau equations
• Persistence of translational symmetry in the BCS model with radial pair interaction
• Bogolubov-Hartree-Fock theory for strongly interacting fermions in the low density limit
• Universality in low-dimensional BCS theory
• Microscopic Derivation of the Ginzburg-Landau Model
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• A lower bound for the BCS functional with boundary conditions at infinity
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• A mathematical derivation of zero-temperature 2D superconductivity from microscopic Bardeen-Cooper-Schrieffer model
• Condensation of fermion pairs in a domain