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Quantum Field Theoretical Methods in Statistical Mechanics

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Statistical Physics II

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 31))

Abstract

We have seen that macroscopic properties in a linear irreversible process are determined by the response function, the relaxation function, the complex admittance or the double-time correlation functions. This chapter briefly describes techniques for calculating these functions. Of course, there are many methods of calculation, each of which has its own merits and demerits and has particular key points to be considered. A simple example for the determination of the response function by using the kinetic theoretical method was given in Chap. 3.

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References

  1. N. N. Bogolyubov, S. V. Tyablikov: Sov. Phys. Dokl. 4,589 (1959)

    ADS  MATH  Google Scholar 

  2. V. L. Bonch-Bruevich, S. V. Tyablikov: The Green Function Method in Statistical Mechanics (North-Holland, Amsterdam 1962)

    MATH  Google Scholar 

  3. D. N. Zubarev: Sov. Phys. Usp. 3,320 (1960)

    Article  MathSciNet  ADS  Google Scholar 

  4. A L. Fetter, J. D. Walecka: Quantum Theory of Many-Particle Systems (McGraw- Hill, New York 1971), pp. 21–25

    Google Scholar 

  5. S. V. Tyablikov: Methods in Quantum Theory of Magnetism (Plenum, New York 1967)

    Google Scholar 

  6. D. Bohm, D. Pines: Phys. Rev. 92,609 (1953);

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. D. Pines: The Many-Body Problems (Benjamin, Reading MA 1962)

    Google Scholar 

  8. L. P. Kadanoff, G. Baym: Quantum Statistical Mechanics (Benjamin Reading MA 1962)

    MATH  Google Scholar 

  9. S. Ichmaru: Rev. Mod. Phys. 54,1017 (1982)

    Article  ADS  Google Scholar 

  10. J. Lindhard: Dan. Mat.-Fys. Medd. 28, No 28 (1954)

    Google Scholar 

  11. E. Wigner: Phys. Rev. 40,749 (1932)

    Article  ADS  MATH  Google Scholar 

  12. Iu. L. Klimontovich: Sov. Phys. JETP 6,753 (1958)

    MathSciNet  ADS  Google Scholar 

  13. A A Vlasov: Zh. Eksp. Teor. Fiz. 8,291 (1938)

    Google Scholar 

  14. L. D. Landau: J. Phys. USSR. 10,25 (1946)

    Google Scholar 

  15. P. Debye, E. Hückel: Phys. Z. 24,185 (1923)

    Google Scholar 

  16. A A Abrikosov, L. P. Gor’kov, I. E. Dzyaloshinskii: Method of Quantum Field Theory in Statistical Mechanics (Prentice-Hall, New York 1963)

    Google Scholar 

  17. J. R. Schrieffer: Theory of Superconductivity (Benjamin, New York 1964)

    MATH  Google Scholar 

  18. G. C. Wick: Phys. Rev. 80,268 (1950)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. R. P. Feynman: Phys. Rev. 76,749, 769 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. T. Matsubara: Prog. Theor. Phys. 14,351 (1955)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. F. J. Dyson: Phys. Rev. 75,486,1736 (1949)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. A A. Abrikosov, L. P. Gor’kov, I. E. Dzyaloshinskii: Sov. Phys. JETP 9, 636 (1959); 10,186(1960)

    Google Scholar 

  23. E S. Fradkin: Sov. Phys. JETP 9,912 (1959)

    MathSciNet  MATH  Google Scholar 

  24. G. Baym, N. D. Mermin: J. Math. Phys. 2,232 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. C. Bloch, C. De Dominicis: Nucl. Phys. 7,459 (1956); 10, 181, 509 (1959)

    Google Scholar 

  26. C. De Dominies, P. Martin: J. Math. Phys. 5, 15, 31 (1964)

    Article  ADS  Google Scholar 

  27. A I. Larkin: Sov. Phys. JETP 10, 186 (1960)

    MathSciNet  Google Scholar 

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© 1985 Springer-Verlag Berlin Heidelberg

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Kubo, R., Toda, M., Hashitsume, N. (1985). Quantum Field Theoretical Methods in Statistical Mechanics. In: Statistical Physics II. Springer Series in Solid-State Sciences, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96701-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-96701-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-96703-0

  • Online ISBN: 978-3-642-96701-6

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