Advertisement

The European Physical Journal B

, Volume 80, Issue 1, pp 41–49 | Cite as

Density dependence of the energy of N Cooper pairs

  • M. Combescot
  • T. Cren
  • M. Crouzeix
  • O. Betbeder-Matibet
Article

Abstract.

We approach the analytical resolution of Richardson’s equations from which the exact energy of N Cooper pairs can be obtained, through an expansion in the dimensionless parameter associated to sample volume. We first derive the explicit solutions of these Richardson’s equations for the lowest N’s, up to fourth order in this parameter. From them, we deduce a compact expression of the N-pair energy, that we recover using a more general procedure. Our results support the recently found fact that the expression of the N-pair energy obtained at the lowest order stays valid up to the dense limit, the next order term being here shown to be underextensive due to a set of non-trivial cancellations.

Keywords

Density Dependence Cooper Pair Potential Layer Grand Canonical Ensemble Pauli Exclusion Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Onnes, The Superconductivity of Mercury (Comm. Phys. Lab., Univ. Leiden, 1911), Nos. 122, 124 Google Scholar
  2. 2.
    H. Frölich, Phys. Rev. 79, 845 (1950) CrossRefADSGoogle Scholar
  3. 3.
    L.N. Cooper, Phys. Rev. 104, 1189 (1956) CrossRefMATHADSGoogle Scholar
  4. 4.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957) CrossRefMATHADSMathSciNetGoogle Scholar
  5. 5.
    R.W. Richardson, Phys. Lett. 3, 277 (1963) CrossRefMATHADSGoogle Scholar
  6. 6.
    R.W. Richardson, N. Sherman, Nucl. Phys. 52, 221 (1964) CrossRefMathSciNetGoogle Scholar
  7. 7.
    R.W. Richardson, J. Math. Phys. 18, 1802 (1977) CrossRefADSGoogle Scholar
  8. 8.
    M. Gaudin, J. Phys. France 37, 1087 (1976) CrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Dukelsky, S. Pittel, G. Sierra, Rev. Mod. Phys. 76, 643 (2004) CrossRefMATHADSMathSciNetGoogle Scholar
  10. 10.
    J.M. Roman, G. Sierra, J. Dukelsky, Nucl. Phys. B 634, 483 (2002) CrossRefMATHADSMathSciNetGoogle Scholar
  11. 11.
    M. Combescot, O. Betbeder-Matibet, F. Dubin, Phys. Rep. 463, 215 (2008) CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    M. Combescot, O. Betbeder-Matibet, Phys. Rev. Lett. 104, 206404 (2010) CrossRefADSGoogle Scholar
  13. 13.
    W. Pogosov, M. Combescot, M. Crouzeix, Phys. Rev. B 81, 174514 (2010) CrossRefADSGoogle Scholar
  14. 14.
    W. Pogosov, M. Combescot, JETP Lett. 92, 534 (2010) CrossRefGoogle Scholar
  15. 15.
    W. Pogosov, M. Combescot, submitted to Phys. Rev. B Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. Combescot
    • 1
  • T. Cren
    • 1
  • M. Crouzeix
    • 2
  • O. Betbeder-Matibet
    • 1
  1. 1.Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRSParis Cedex 05France
  2. 2.Institut de Recherches Mathématiques de Rennes, Université de Rennes 1Rennes CedexFrance

Personalised recommendations