We show that the energy gap for the BCS gap equation is Ξ=μ(8e−2+o(1))exp(π2μ−−√a) in the low density limit μ→0. Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.
Letters in Mathematical Physics
Most of this work was done as part of the author’s master’s thesis. The author would like to thank Jan Philip Solovej for his supervision of this process. Open Access funding provided by Institute of Science and Technology (IST Austria)
Lauritsen AB. The BCS energy gap at low density. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01358-5
Lauritsen, A. B. (2021). The BCS energy gap at low density. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01358-5
Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01358-5.
A. B. Lauritsen, “The BCS energy gap at low density,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021.
Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical Physics. 111, 20.
Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” Letters in Mathematical Physics, vol. 111, 20, Springer Nature, 2021, doi:10.1007/s11005-021-01358-5.
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