2007/03/31 by Christian Hainzl, Eman Hamza, Robert Seiringer +1 · 6 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Physics of Superconductivity and Magnetism #cond-mat.supr-con #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-008-0489-2
published as Commun. Math. Phys. 281, 349-367 (2008) · Revised Version. To appear in Commun. Math. Phys.
arxiv created 2007/11/21 · openalex publication_date 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.