Advertisement

Pairing and BCS Theory in an Exactly-Soluble Many Fermion Model

  • C. Esebbag
  • M. de Llano
  • R. M. Carter
Part of the Condensed Matter Theories book series (COMT, volume 8)

Abstract

We consider the exactly soluble one-dimensional (1D) fermion fluid1 with pair-wise attractive delta interactions for two main reasons. Firstly, in the case of two distinct fermion species (for example the two spin states of the electron) dynamical similarities exist between the present 1D model and 3D electron fluid jellium model. In particular for weak coupling the model reproduces the essential singularity familiar from standard 3D low-temperature superconductivity2.

Keywords

Critical Temperature Cooper Pair Bose Condensation Quasiparticle Energy Pair Binding Energy 
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.
    J. B. McGuire, “State function and spectral properties of a two-component interacting Fermi gas,” J. Math. Phys. 31:164 (1990).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    M. Casas, C. Esebbag, A. Extremera, J. M. Getino, M. de Llano, A. Piastino and H. Rubio, “Cooper pairing in a soluble one-dimensional many-fermion model,” Phys. Rev. A 44:4415 (1991).ADSCrossRefGoogle Scholar
  3. 3.
    M. Randeria, J.-M. Duan and L.-Y. Shieh, “Bound States, Cooper Pairing and Bose Condensation in Two Dimensions,” Phys. Rev. Lett. 62:981 (1989)ADSCrossRefGoogle Scholar
  4. M. Randeria, J.-M. Duan and L.-Y. Shieh, “Bound States, Cooper Pairing and Bose Condensation in Two Dimensions,” Phys. Rev. Lett. 62:2887(E) (1989).ADSGoogle Scholar
  5. M. Randeria, J.-M. Duan and L.-Y. Shieh, “Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation,” Phys. Rev. B 41:327 (1990).ADSCrossRefGoogle Scholar
  6. K Miyake, “Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film,” Prog. Theor. Phys. 69:1794 (1983).ADSCrossRefGoogle Scholar
  7. 4.
    P. Noziéres and S. Schmitt-Rink, “Bose Condensation in an Attractive Fermion Gas: From Weak to Strong Coupling Superconductivity,” J. Low Temp. Phys. 59:195 (1985).ADSCrossRefGoogle Scholar
  8. 5.
    R. Micnas, J. Ranninger and S. Robaskiewicz, “Superconductivity in narrow-band systems with local nonretarded attractive interactions,” Rev. Mod. Phys. 62:113 (1990).ADSCrossRefGoogle Scholar
  9. 6.
    Y. J. Uemura et al, “Basic Similarites among Cuprate, Bismuthate, Organic, Chevrel-Phase, and Heavy-Fermion Superconductors Shown by Penetration-Depth Measurements,” Phys. Rev. Lett. 66:2665 (1991)ADSCrossRefGoogle Scholar
  10. “Magnetic-field penetration depth in K3C60 mesaured by muon spin relaxation,” Nature 352:605 (1991).Google Scholar
  11. 7.
    J. Bardeen, L. N. Cooper and J. Schrieffer, “Theory of Superconductivity,” Phys. Rev. 108:1175 (1957).MathSciNetADSMATHCrossRefGoogle Scholar
  12. 8.
    M. Gaudin, “Un Systeme a une dimension de fermions en interaction,” Phys. Lett. A 24:55 (1967).ADSCrossRefGoogle Scholar
  13. 9.
    S. Schmitt-Rink, C. M. Varma and A. E. Ruckenstein, “Pairing in Two Dimensions,” Phys. Rev. Lett. 44:445 (1989)ADSCrossRefGoogle Scholar
  14. J. W. Serene, “Stability of two-dimensional Fermi liquids against pair fluctuations with large total momentum,” Phys. Rev. B 40:10873 (1989)ADSCrossRefGoogle Scholar
  15. A. Tokumitu, K. Miyake and K. Yamada, “Crossover between Cooper-Pair Condenstaion and Bose-Einstein Condensation of ‘Di-Electronic Molecules’ in Two-Dimensional Superconductors,” Prog. Theor. Phys. 106:63 (1991).CrossRefGoogle Scholar
  16. 10.
    A. L. Fetter and J. D. Walecka, “Quantum Theory of Many Particle Systems,” McGraw-Hill, New York (1971), p. 330ff.Google Scholar
  17. 11.
    M. Girardeau, “Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension,” J. Math. Phys. 1:516 (1960).MathSciNetADSMATHCrossRefGoogle Scholar
  18. 12.
    C. Esebbag, M de Llano and R. M. Quick, “Test of Bardeen-Cooper-Schrieffer theory in an exactly soluble many-fermion model,” University of Pretoria preprint (1992).Google Scholar
  19. 13.
    G. Gutierrez and A. Piastino “A Systematic Approach to the Hartree-Fock Problem in the Thermodynamic Limit,” Ann. Phys. 133:332 (1981).ADSCrossRefGoogle Scholar
  20. 14.
    C. Esebbag, J. M. Getino, M. de Llano, S. A. Moszowski, U. Oseguera, A. Piastino and H. Rubio, “Cooper pairing in one, two, and three dimensions,” J. Math Phys. 33:1221 (1992).MathSciNetADSCrossRefGoogle Scholar
  21. 15.
    R. K. Pathria, “Statistical Mechanics,” Pergamon Press, Oxford (1984).Google Scholar
  22. 16.
    D. S. Fisher and P. C. Hohenberg, “Dilute Bose gas in two dimensions,” Phys. Rev. B. 37:4936 (1988).ADSCrossRefGoogle Scholar
  23. 17.
    P.C. Hohenberg, “Existence of Long-Range Order in One and Two Dimensions,” Phys. Rev. 158:33 (1967).CrossRefGoogle Scholar
  24. 18.
    J.M. Luttinger and H. K. Sy, “Bose-Einstein Condensation in a One-Dimensional Model with Random Impurities,” Phys. Rev. A. 7:712 (1973).ADSCrossRefGoogle Scholar
  25. 19.
    R. Friedberg and T. D. Lee, “Gap energy and long-range order in the boson-fermion model of superconductivity,” Phys. Rev. B. 40:6745 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • C. Esebbag
    • 1
  • M. de Llano
    • 2
  • R. M. Carter
    • 2
  1. 1.Departamento de Física TeóricaUniversidad Autónoma de MadridMadridSpain
  2. 2.Department of PhysicsUniversity of PretoriaPretoriaSouth Africa

Personalised recommendations