Advertisement

Journal of Low Temperature Physics

, Volume 129, Issue 5–6, pp 219–262 | Cite as

Introduction to Ginzburg-Landau and Gross-Pitaevskii Theories for Superconductors and Superfluids

  • Nikolai B. Kopnin
Article

Abstract

An elementary overview is given of the most frequently used models in the theory of superfluidity and superconductivity. The Gross-Pitaevskii, Ginzburg-Landau and time-dependent Ginzburg-Landau equations are derived, and their conditions of applicability are discussed. Some applications are considered including the critical current and vortices.

Keywords

Vortex Magnetic Material Critical Current Elementary Overview 
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.
    V.L. Ginzburg, V. L. and L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950); in: L.D. Landau, Collected Papers (Pergamon Press, 1965).Google Scholar
  2. 2.
    A.P. Levaniuk, Zh. Eksp. Teor. Fiz. 36, 810 (1959) [Sov. Phys. JETP 9, 571 (1960)].Google Scholar
  3. 3.
    V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960) [Sov. Phys. Solid State 2, 1824 (1961)].Google Scholar
  4. 4.
    L. P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).Google Scholar
  5. 5.
    E. P. Gross, Il Nouvo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963).Google Scholar
  6. 6.
    J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).Google Scholar
  7. 7.
    L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 36, 1918 (1959).Google Scholar
  8. 8.
    L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 37, 1407 (1959).Google Scholar
  9. 9.
    L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon Press, 1959).Google Scholar
  10. 10.
    P.G. de Gennes, Superconductivity of Metals and Alloys (W.A. Benjamin, Inc, 1965).Google Scholar
  11. 11.
    V.L. Ginzburg and L.P. Pitaevskii, Zh. Eksp. Teor. Phys. 34, 1240 (1958) [Sov. Phys. JETP 7, 858 (1958)]; L.P. Pitaevskii, Zh. Eksp. Teor. Phys. 35, 408 (1958) [Sov. Phys. JETP 8, 282 (1959)].Google Scholar
  12. 12.
    V.L. Ginzburg and A. A. Sobyanin, J. Low Temp. Phys. 49, 507 (1982).Google Scholar
  13. 13.
    R.J. Donnelly, Quantized vortices in Helium II (Cambridge University Press, Cambridge, UK, 1991).Google Scholar
  14. 14.
    R. Feynman, in: Progress in Low Temperature Physics Vol. 1, edited by C. J. Gorter (North Holland, Amsterdam, 1955) p. 36.Google Scholar
  15. 15.
    A.A. Abrikosov, Zh. Eksp. Teor. Fiz. 32, 1442 (1957) [Sov. Phys. JETP 5, 1174 (1957)].Google Scholar
  16. 16.
    W.H. Kleiner, L.M. Roth, and S.H. Autler, Phys. Rev. 133 A, 1226 (1964).Google Scholar
  17. 17.
    A. A. Abrikosov, Fundamentals of The Theory of Metals (North Holland, Amsterdam, 1998).Google Scholar
  18. 18.
    D. Saint-James, G. Sarma, and E.J. Thomas, Type II superconductivity (Pergamon Press, 1969).Google Scholar
  19. 19.
    A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).Google Scholar
  20. 20.
    N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford University Press, 2001).Google Scholar
  21. 21.
    A. Schmid, Phys. Kond. Materie 5, 302 (1966).Google Scholar
  22. 22.
    E. Abrahams and T. Tsuneto, Phys. Rev. 152, 416 (1966).Google Scholar
  23. 23.
    P. Wölfle and D. Vollhardt, The Superfluid Phases of Helium 3 (Taylor and Francis, London, New York, 1990).Google Scholar
  24. 24.
    V. P. Mineev and K. V. Samokhin, Introduction to Nonconventional Superconductivity (Gordon and Breach, New York, 1999).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Nikolai B. Kopnin
    • 1
    • 2
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHUTFinland
  2. 2.L. D. Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations