Critical temperature and energy gap for the BCS equation Journal Article

Author(s): Hainzl, Christian; Seiringer, Robert
Article Title: Critical temperature and energy gap for the BCS equation
Abstract: 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).
Journal Title: Physical Review B - Condensed Matter and Materials Physics
Volume: 77
Issue 18
ISSN: 1550-235X
Publisher: American Physical Society  
Date Published: 2008-05-28
Start Page: Article number: 184517
DOI: 10.1103/PhysRevB.77.184517
Open access: yes (repository)
IST Austria Authors
  1. Robert Seiringer
    123 Seiringer
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