Communications in Mathematical Physics

, Volume 281, Issue 2, pp 349–367 | Cite as

The BCS Functional for General Pair Interactions

  • Christian Hainzl
  • Eman Hamza
  • Robert Seiringer
  • Jan Philip Solovej
Article

Abstract

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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Copyright information

© The Authors 2008

Authors and Affiliations

  • Christian Hainzl
    • 1
  • Eman Hamza
    • 2
  • Robert Seiringer
    • 3
  • Jan Philip Solovej
    • 4
  1. 1.Departments of Mathematics and PhysicsUABBirminghamUSA
  2. 2.Department of MathematicsUABBirminghamUSA
  3. 3.Department of PhysicsPrinceton UniversityPrincetonUSA
  4. 4.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark

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