Critical Temperature and Energy Gap for the BCS Equation

@article{Hainzl2008CriticalTA,
  title={Critical Temperature and Energy Gap for the BCS Equation},
  author={C. Hainzl and R. Seiringer},
  journal={Physical Review B},
  year={2008},
  volume={77},
  pages={184517}
}
We derive upper and lower bounds on the critical temperature Tc and the energy gap � (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two- body interaction potentialV (x). At weak coupling � ≪ 1 and under appropriate assumptions on V (x), our bounds show that Tc ∼ Aexp(−B/�) and � ∼ C exp(−B/�) 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… Expand
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