Critical temperature and energy gap for the BCS equation

C. Hainzl, R. Seiringer, Physical Review B - Condensed Matter and Materials Physics 77 (2008).


Journal Article | Published
Author
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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).
Publishing Year
Date Published
2008-05-28
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Volume
77
Issue
18
IST-REx-ID

Cite this

Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation. Physical Review B - Condensed Matter and Materials Physics. 2008;77(18). doi:10.1103/PhysRevB.77.184517
Hainzl, C., & Seiringer, R. (2008). Critical temperature and energy gap for the BCS equation. Physical Review B - Condensed Matter and Materials Physics, 77(18). https://doi.org/10.1103/PhysRevB.77.184517
Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” Physical Review B - Condensed Matter and Materials Physics 77, no. 18 (2008). https://doi.org/10.1103/PhysRevB.77.184517.
C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS equation,” Physical Review B - Condensed Matter and Materials Physics, vol. 77, no. 18, 2008.
Hainzl C, Seiringer R. 2008. Critical temperature and energy gap for the BCS equation. Physical Review B - Condensed Matter and Materials Physics. 77(18).
Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” Physical Review B - Condensed Matter and Materials Physics, vol. 77, no. 18, American Physical Society, 2008, doi:10.1103/PhysRevB.77.184517.

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