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

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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.

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REFERENCES

  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. A.P. Levaniuk, Zh. Eksp. Teor. Fiz. 36, 810 (1959) [Sov. Phys. JETP 9, 571 (1960)].

    Google Scholar 

  3. V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960) [Sov. Phys. Solid State 2, 1824 (1961)].

    Google Scholar 

  4. L. P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961).

    Google Scholar 

  5. E. P. Gross, Il Nouvo Cimento 20, 454 (1961); J. Math. Phys. 4, 195 (1963).

    Google Scholar 

  6. J. Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).

    Google Scholar 

  7. L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 36, 1918 (1959).

    Google Scholar 

  8. L.P. Gor'kov, Zh. Eksp. Teor. Fiz. 37, 1407 (1959).

    Google Scholar 

  9. L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon Press, 1959).

  10. P.G. de Gennes, Superconductivity of Metals and Alloys (W.A. Benjamin, Inc, 1965).

  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. V.L. Ginzburg and A. A. Sobyanin, J. Low Temp. Phys. 49, 507 (1982).

    Google Scholar 

  13. R.J. Donnelly, Quantized vortices in Helium II (Cambridge University Press, Cambridge, UK, 1991).

    Google Scholar 

  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. A.A. Abrikosov, Zh. Eksp. Teor. Fiz. 32, 1442 (1957) [Sov. Phys. JETP 5, 1174 (1957)].

    Google Scholar 

  16. W.H. Kleiner, L.M. Roth, and S.H. Autler, Phys. Rev. 133 A, 1226 (1964).

    Google Scholar 

  17. A. A. Abrikosov, Fundamentals of The Theory of Metals (North Holland, Amsterdam, 1998).

    Google Scholar 

  18. D. Saint-James, G. Sarma, and E.J. Thomas, Type II superconductivity (Pergamon Press, 1969).

  19. A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).

    Google Scholar 

  20. N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford University Press, 2001).

  21. A. Schmid, Phys. Kond. Materie 5, 302 (1966).

    Google Scholar 

  22. E. Abrahams and T. Tsuneto, Phys. Rev. 152, 416 (1966).

    Google Scholar 

  23. P. Wölfle and D. Vollhardt, The Superfluid Phases of Helium 3 (Taylor and Francis, London, New York, 1990).

    Google Scholar 

  24. V. P. Mineev and K. V. Samokhin, Introduction to Nonconventional Superconductivity (Gordon and Breach, New York, 1999).

    Google Scholar 

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Authors and Affiliations

  1. Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015, HUT, Finland

    Nikolai B. Kopnin

  2. L. D. Landau Institute for Theoretical Physics, 117940, Moscow, Russia

    Nikolai B. Kopnin

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  1. Nikolai B. Kopnin
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Kopnin, N.B. Introduction to Ginzburg-Landau and Gross-Pitaevskii Theories for Superconductors and Superfluids. Journal of Low Temperature Physics 129, 219–262 (2002). https://doi.org/10.1023/A:1021456311824

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