Translation-invariant quasi-free states for fermionic systems and the BCS approximation

Abstract

We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but includes also direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity.

31 pages, 2 figures

References in corpus (5)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• A Nonlinear Model for Relativistic Electrons at Positive Temperature
• The BCS Critical Temperature for Potentials with Negative Scattering Length
• A Numerical Perspective on Hartree-Fock-Bogoliubov Theory

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• The BCS functional of superconductivity and its mathematical properties
• The Bogoliubov free energy functional I. Existence of minimizers and phase diagram
• Multi-component Ginzburg-Landau theory: microscopic derivation and examples
• Persistence of translational symmetry in the BCS model with radial pair interaction
• The BCS Energy Gap at Low Density
• 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
• Mixed parity pairing in a dipolar gas
• A lower bound for the BCS functional with boundary conditions at infinity