2008/01/31 by Christian Hainzl, Robert Seiringer · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.supr-con #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.77.184517
published as Phys. Rev. B 77, 184517 (2008) · RevTeX4, 23 pages. Revised version, to appear in Phys. Rev. B
arxiv created 2008/05/23 · arxiv updated 2009/12/01
We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ≪ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼ A exp(-B/λ) and Ξ∼ C exp(-B/λ) for some explicit coefficients A, B and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).