TY - JOUR
AB - 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.
AU - Hainzl, Christian
AU - Hamza, Eman
AU - Robert Seiringer
AU - Solovej, Jan P
ID - 2380
IS - 2
JF - Communications in Mathematical Physics
TI - The BCS functional for general pair interactions
VL - 281
ER -