Advertisement

Perturbation Theory of Response Functions

  • J. W. Halley
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 35)

Abstract

The chapter by Dr. Stinchcombe has established connections between functions defined as
$$\begin{gathered} G_r (t,t') = < < A(t);B(t') > > _r \hfill \\ = - i\theta (t - t') < \left[ {A(t),B(t')} \right]_\eta > \hfill \\ \end{gathered}$$
and scattering cross-sections and susceptibilities observed directly in experiments on condensed matter.

Keywords

Perturbation Theory Response Function Creation Operator Perturbation Series Dyson Equation 
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.
    C.E. Campbell and E. Feenberg, Phys. Rev. 188, 396 (1969)ADSCrossRefGoogle Scholar
  2. 1a.
    H. W. Jackson, Phys. Rev. A8, 1529 (1973)ADSGoogle Scholar
  3. 1b.
    R. Hastings and J. W. Halley, Phys. Rev. A10, 2488 (1974).ADSGoogle Scholar
  4. 2.
    A. D. B. Woods and R. A. Cowley, Rep. Prog, in Phys. 36, 1135 (1973)ADSCrossRefGoogle Scholar
  5. 2a.
    P. Kleban and J. W. Halley, Phys. Rev. B11, 3520 (1975).ADSGoogle Scholar
  6. 3.
    R. Loudon, Adv. in Phys. 13, 423 (1964).ADSCrossRefGoogle Scholar
  7. 4.
    P. Kleban, Phys. Lett. A49, 19 (1974)ADSGoogle Scholar
  8. 4a.
    P. Kleban and R. Hastings, Phys. Rev. B11, 1878 (1975).ADSGoogle Scholar
  9. 5.
    F. Pinski and C. Campbell, to be published.Google Scholar
  10. 6.
    A. A. Abrikosov, L. P. Gorkov and I. E. Dzialoskinski, Methods of Quantum Field Theory in Statistical Physics, trans, by R. A. Silverman, Prentice-Hall, Englewood Cliffs, N.J. (1963).MATHGoogle Scholar
  11. 7.
    A. Fetter and D. Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill, N.Y. (1971).Google Scholar
  12. 8.
    P. Nozieres, Theory of Interacting Fermi Systems, W. A. Benjamin, N. Y. (1964).MATHGoogle Scholar
  13. 3.
    D. N. Zubarev, Usp. Fiz. Nauk. 71, 71–116 (1960) (Sov. Phys. -Uspekhi 3, 320 (1960)).MathSciNetGoogle Scholar
  14. 10.
    This is done for the weakly interacting Bose gas in section of Reference 7.Google Scholar
  15. 11.
    M. Stephen, Phys. Rev. 187, 279 (1969).ADSCrossRefGoogle Scholar
  16. 12.
    D. Pines, Elementary Excitations in Solids, W. A. Benjamin, N.Y. (1964).MATHGoogle Scholar
  17. 13.
    J. Lindhard, Kgl. Danske Videnskab. Selskab, Mat-fys. Medd. 28, 8 (1954).MathSciNetGoogle Scholar
  18. 14.
    T. Kawasaki, J. Phys. Soc. Jap. 29, 1144 (1970).ADSCrossRefGoogle Scholar
  19. 15.
    See Chapter 6 of Reference 8 for a more thorough discussion of this point.Google Scholar
  20. 16.
    A. Zawadowski, J. Ruvalds, J. Solana, Phys. Rev. A5, 399 (1972) and two last references in 1.ADSGoogle Scholar
  21. 17.
    P. Kleban and R. Hastings, Phys. Rev. B11, 1878 (1975).ADSGoogle Scholar
  22. 18.
    See first reference in 16.Google Scholar
  23. 19.
    Reference 12.Google Scholar
  24. 20.
    M. H. Cohen and J. Ruvalds, Phys. Rev. Lett. 23, 1378 (1969)ADSCrossRefGoogle Scholar
  25. 20a.
    J. Ruvalds and A. Zawadowski, Phys, Rev. B2, 1172 (1970).ADSGoogle Scholar
  26. 21.
    R. Tubino and J. Birman, Phys. Rev. Lett. 35, 670 (1975).ADSCrossRefGoogle Scholar
  27. 22.
    S. Go, H. Bilz and M. Cardona, Phys. Rev. Lett. 34, 580 (1975).ADSCrossRefGoogle Scholar
  28. 23.
    A. A. Maradudin, in Phonons (edited by M. Nusimovici), p. 427, Flammarion, Paris (1971).Google Scholar
  29. 24.
    M. G. Cottam and R. B. Stinchcombe, Phys. C: Sol. St. Phys. 3, 2283–304 (1970), and the article by Cottam in this volume.ADSCrossRefGoogle Scholar
  30. 25.
    J. W. Halley and R. Hastings, Phys. Rev. B15, 1404 (1977) and the article by Hastings in this volume.ADSGoogle Scholar
  31. 26.
    Chapter 5 of Reference 6.Google Scholar
  32. 27.
    Reference 6.Google Scholar
  33. 28.
    Chapter 7 of Reference 6; Chapter 7 of Reference 8. G. M. Eliashberg, Sov. Phys. JETP 13, 333 (1971)Google Scholar
  34. 28a.
    B. I. Ivlev, S. G. Lisityn, S. G. Lisityn and G. M. Eliashberg, J. Low Temp. Phys. 10, 449 (1973).ADSCrossRefGoogle Scholar
  35. 29.
    D. Rainer and J. W. Serene, Phys. Rev. B13, 4745 (1976),ADSGoogle Scholar
  36. 30.
    Chapter 5 of Reference 6.Google Scholar
  37. 31.
    E. Feenberg, The Theory of Quantum Fluids, Academic Press, N.Y. (1969).Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • J. W. Halley
    • 1
  1. 1.University of MinnesotaMinneapolisUSA

Personalised recommendations