The BCS Energy Gap at Low Density

Abstract

We show that the energy gap for the BCS gap equation is $\Xi =\mu \left(8e^{-2}+o(1)\right)\exp \left(\frac{\pi }{2\sqrt{\mu }a}\right)$ in the low density limit $\mu \to 0$. Together with the similar result for the critical temperature [arXiv:0803.3324] 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.

arXiv comment12 pages

References in corpus (6)

• Critical Temperature and Energy Gap for the BCS Equation
• The BCS Functional for General Pair Interactions
• The BCS functional of superconductivity and its mathematical properties
• The BCS Critical Temperature for Potentials with Negative Scattering Length
• Spectral properties of the BCS gap equation of superfluidity
• Translation-invariant quasi-free states for fermionic systems and the BCS approximation

Cited by in corpus (4)

• The BCS Critical Temperature at High Density
• The BCS Energy Gap at High Density
• Universality in low-dimensional BCS theory
• Dynamics of mean-field Fermi systems with nonzero pairing