The BCS Model for General Pair Interactions
Christian Hainzl, Eman Hamza, Robert Seiringer, Jan Philip Solovej · arXiv (Cornell University) · 2007
Abstract. We present a rigorous analysis of the Bardeen-Cooper-Schrieffer (BCS) model 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 effective linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractivepotentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential. 1.