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The BCS functional for general pair interactions. (English) Zbl 1161.82027
This paper deals with the study of the Bardeen-Cooper-Schrieffer regime, in the case where the interaction potentials are local for atomic Fermi gases. The mathematical framework is described by a functional, initially derived by Leggett. The main purpose of the present paper is to obtain necessary and sufficient conditions on pair interaction potentials such that the system behaves a superfluid behavior. The authors deduce the existence of a critical temperature below which the Bardeen-Cooper-Schrieffer pairing wave function does not vanish identically. The arguments developed in this paper combine variational techniques with related L p estimates.

82D55Superconductors (statistical mechanics)
82B10Quantum equilibrium statistical mechanics (general)
[1]Andrenacci N., Perali A., Pieri P., Strinati G.C.: Density-induced BCS to Bose-Einstein crossover. Phys. Rev. B 60, 12410 (1999) · doi:10.1103/PhysRevB.60.12410
[2]Bach V., Lieb E., Solovej J.: Generalized Hartree-Fock theory and the Hubbard model. J. Stat. Phys. 76, 3–89 (1994) · doi:10.1007/BF02188656
[3]Bardeen J., Cooper L., Schrieffer J.: Theory of Superconductivity. Phys. Rev. 108, 1175–1204 (1957) · Zbl 0090.45401 · doi:10.1103/PhysRev.108.1175
[4]Billard P., Fano G.: An existence proof for the gap equation in the superconductivity theory. Commun. Math. Phys. 10, 274–279 (1968)
[5]Bloch, I., Dalibard, J., Zwerger, W.: Many-Body Physics with Ultracold Gases. http://arxiv.org/abs/:0704.3011 , 2007, to appear in Rev. Mod. Phys.
[6]Carlson J., Chang S.-Y., Pandharipande V.R., Schmidt K.E.: Superfluid Fermi Gases with Large Scattering Length. Phys. Rev. Lett. 91, 0504011 (2003)
[7]Chen Q., Stajic J., Tan S., Levin K.: BCS–BEC crossover: From high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005) · doi:10.1016/j.physrep.2005.02.005
[8]Fetter A., Walecka J.D.: Quantum theory of many-particle systems. McGraw-Hill, New-York (1971)
[9]Frank R.L., Hainzl C., Naboko S., Seiringer R.: The critical temperature for the BCS equation at weak coupling. J. Geom. Anal. 17, 559–568 (2007)
[10]Leggett, A.J.: Diatomic Molecules and Cooper Pairs. Modern trends in the theory of condensed matter, J. Phys. (Paris) Colloq, C7–19 Bertin-Heidelberg-New York: Springer, 1980
[11]Lieb, E., Loss, M.: Analysis. Providence RI: Amer. Math. Soc., 2001
[12]Martin P.A., Rothen F.: Many-body problems and Quantum Field Theory. Springer, Berlin-Heidelberg-New York (2004)
[13]McLeod J.B., Yang Y.: The uniqueness and approximation of a positive solution of the Bardeen-Cooper-Schrieffer gap equation. J. Math. Phys. 41, 6007–6025 (2000)
[14]Nozières P., Schmitt-Rink S.: Bose Condensation in an Attractive Fermion Gas: From Weak to Strong Coupling Superconductivity. J. Low Temp. Phys. 59, 195–211 (1985)
[15]Parish M., Mihaila B., Timmermans E., Blagoev K., Littlewood P.: BCS-BEC crossover with a finite-range interaction. Phys. Rev. B 71, 0645131–0645136 (2005) · doi:10.1103/PhysRevB.71.064513
[16]Randeria, M.: In: Bose-Einstein Condensation, Griffin, A., Snoke, D.W., Stringari, S. eds., Cambridge: Cambridge University Press, 1995
[17]Tiesinga E., Verhaar B.J., Stoof H.T.C.: Threshold and resonance phenomena in ultracold ground-state collisions. Phys. Rev. A 47, 4114 (1993) · doi:10.1103/PhysRevA.47.4114
[18]Vansevenant A.: The gap equation in superconductivity theory. Physica 17D, 339–344 (1985)
[19]Yang Y.: On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity. Lett. Math. Phys. 22, 27–37 (1991) · Zbl 0729.45009 · doi:10.1007/BF00400375