Abstract
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential.
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Communicated by H. Spohn
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Hainzl, C., Hamza, E., Seiringer, R. et al. The BCS Functional for General Pair Interactions. Commun. Math. Phys. 281, 349–367 (2008). https://doi.org/10.1007/s00220-008-0489-2
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DOI: https://doi.org/10.1007/s00220-008-0489-2