The BCS Functional for General Pair Interactions

Details The BCS Functional for General Pair Interactions The BCS Functional for General Pair Interactions

2007-03-29

arxiv.org/abs/math-ph/0703086v2

Commun. Math. Phys. 281, 349-367 (2008)

Physics

Mathematical Physics

Revised Version. To appear in Commun. Math. Phys.

Scientific paper

10.1007/s00220-008-0489-2

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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