The BCS Model for General Pair Interaction

TY - JOUR

T1 - The BCS Model for General Pair Interaction

AU - Hainzl, Christian

AU - Hamza, Eman

AU - Seiringer, Robert

AU - Solovej, Jan Philip

PY - 2008/6/2

Y1 - 2008/6/2

N2 - 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.

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.

M3 - Journal article

SN - 0010-3616

VL - 281

SP - 349

EP - 367

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -