Critical temperature and energy gap for the BCS equation
Hainzl, Christian
Robert Seiringer
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).
American Physical Society
2008
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doc-type:article
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/2376
Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2008;77(18). doi:<a href="https://doi.org/10.1103/PhysRevB.77.184517">10.1103/PhysRevB.77.184517</a>
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevB.77.184517
info:eu-repo/semantics/openAccess