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TDHF-like equations in field theory and condensed matter systems

  • VII. Related Approches
  • Conference paper
  • First Online:
Time-Dependent Hartree-Fock and Beyond

Part of the book series: Lecture Notes in Physics ((LNP,volume 171))

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Abstract

We discuss qualitatively a number of examples of TDHF-like equations that have arisen in model field theories and in (more physically relevant) quasi-one-dimensional condensed matter systems. These examples illustrate several phenomena seen in the (technically much more complicated) applications to nuclear physics and offer a new and perhaps invigorating perspective on TDHF.

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References and footnotes

  1. D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974).

    Google Scholar 

  2. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett 42, 1698 (1979)

    Google Scholar 

  3. — Phys. Rev. B22, 2099 (1980).

    Google Scholar 

  4. D. K. Campbell and Y.-T. Liao, Phys. Rev. D14, 2093 (1976).

    Google Scholar 

  5. R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D12 2443 (1975).

    Google Scholar 

  6. In one space dimension the Dirac y matrices can be represented by the Pauli matrices, a.. Note that, following the conventions in the literature, we use different representations for the y matrices in the Gross-Neveu model and in the continuum electron-phonon model of polyacetylene. Hence the components of the wave functions in the two cases are linear combinations of each other.

    Google Scholar 

  7. J. F. Schonfeld, Nucl. Phys. B95, 148 (1975); R. G. Root, Phys. Rev. D11, 831 (1975).

    Google Scholar 

  8. T. D. Lee and G. C. Wick, Phys. Rev. D9, 2291 (1974).

    Google Scholar 

  9. P. Bonche, S. Koonin, and J. W. Negele, Phys. Rev. C13, 1226 (1976).

    Google Scholar 

  10. A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. 72B, 481 (1978); Ann. Phys. 20, 91 (1979).

    Google Scholar 

  11. R. Shankar and E. Witten, Nucl. Phys. B141, 349 (1978); E. Witten, Nucl. Phys. B142, 285 (1978).

    Google Scholar 

  12. V. E. Zakharov and A. V. Mikhailov, Commun. Math. Phys. 74, 21 (1980).

    Google Scholar 

  13. A. Neveu and N. Papanicolaou, Commun. Math. Phys. 58, 31 (1978).

    Google Scholar 

  14. J. Hirsch, D. Scalapino, and R. Sugar, in progress.

    Google Scholar 

  15. A. R. Bishop, D. K. Campbell, and K. Fesser, Phys. Rev. B, to be published.

    Google Scholar 

  16. For recent review see articles in Proc. Int. Conf. on Low-Dimensional Synthetic Metals (Helsingor, Denmark, August 1980) in Chemica Scripta 17 (1981); Physics in One Dimension, eds. J. Bernasconi and T. Schneider (Springer Verlag, 1981); and A. J. Heeger and A. G. MacDiarmid, p. 353–391 in The Physics and Chemistry of Low Dimensional Solids; ed. L. Alcâcer (Reidel, 1980).

    Google Scholar 

  17. W. P. Su and J. R. Schrieffer, Proc. Nat. Acad. Sci. 77, 5526 (1980).

    Google Scholar 

  18. S. Brazovskii, JETP Lett. 28 606 (1978) (ZhETF Pisma 28, 656 (1978)). JETP (Sov. Phys.) 51 342 (1980) (ZhETF (USSR) 78, 677 (1980)).

    Google Scholar 

  19. H. Takayama, Y. R. Lin-Liu, and K. Maki, Phys. Rev. B21 2388 (1980).

    Google Scholar 

  20. J. A. Krumhansl, B. Horovitz, and A. J. Heeger, Solid State Comm. 34, 945 (1980).

    Google Scholar 

  21. B. Horovitz, Solid State Comm. 34, 61 (1980); Phys. Rev. Lett. 46 742 (1981); Phys. Rev. B22 1101 (1980).

    Google Scholar 

  22. S. Brazovskii and N. Kirova, JETP Lett. 33, 4 (1981) (ZhETF Pisma 33, 6 (1981).

    Google Scholar 

  23. D. K. Campbell and A. R. Bishop, Phys. Rev. B 24, 4859 (1981); Nucl. Phys. B200 (FS4), 297 (1982).

    Google Scholar 

  24. J. E. Hirsch and E. Fradkin, to be published (preprint NSF-ITP-82-34).

    Google Scholar 

  25. R. Jackiw and J. R. Schrieffer, Nucl. Phys. B190 (FS3), 253 (1982).

    Google Scholar 

  26. T. Holstein, Ann. Phys. 8, 325 (1959); Mol. Cryst. Liq. Cryst. 77, 235(1981); T. Holstein and L. Turkevich, Phys. Reports (to be published).

    Google Scholar 

  27. R. A. Cowley, Adv. in Phys. 29, 1 (1980); A. D. Bruce, Adv. in Phys. 29, 111 (1980); A. Bruce and R. Cowley, Adv. in Physics 29, 218 (1980).

    Google Scholar 

  28. M. J. Rice, Phys. Lett. 71A, 152 (1979); M. J. Rice and J. Timonen, Phys. Lett. 73A, 368 (1979); E. J. Mele and M. J. Rice, Chemica Scripta 17, 21 (1981).

    Google Scholar 

  29. D. K. Campbell, p. 674 in Nuclear Physics with Hea Ions and Mesons, Les Houches Session XXX, 1977, R. Balian, et al., eds. North Holland, 1978).

    Google Scholar 

  30. D. K. Campbell, Ann. Phys. 129, 249 (1980).

    Google Scholar 

  31. D. K. Campbell, J. W. Negele, and M. Soldate, unpublished.

    Google Scholar 

  32. A. E. Kudryavtsev, JETP Lett. 22, 82 (1975).

    Google Scholar 

  33. B. S. Getmanov, JETP Lett. 24, 291 (1976).

    Google Scholar 

  34. V. G. Makhankov, Phys. Rep. 35C, 1 (1978).

    Google Scholar 

  35. M. J. Ablowitz, M. D. Kruskal, and J. F. Ladik, SIAM Journ. App. Math. 36 478 (1979).

    Google Scholar 

  36. T. Sugiyama, Prog. Theor. Phys. 61, 1550 (1979).

    Google Scholar 

  37. R. Klein, W. Hasenfratz, N. Theodorakopoulos, and W. Wünderlich, Ferroelectrics 26, 721 (1980).

    Google Scholar 

  38. M. Moshir, Nuc. Phys. B185, 318 (1981).

    Google Scholar 

  39. C. A. Wingate, SIAM Journ. App. Math., in press.

    Google Scholar 

  40. 39. D. K. Campbell, J. Schonfeld, C. A. Wingate, in preparation.

    Google Scholar 

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Authors and Affiliations

  1. Los Alamos National Laboratory, Center for Nonlinear Studies and Theoretical Division, 87545, Los Alamos, New Mexico

    David K. Campbell

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  1. David K. Campbell
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Editor information

K. Goeke P. -G. Reinhard

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© 1982 Springer-Verlag

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Campbell, D.K. (1982). TDHF-like equations in field theory and condensed matter systems. In: Goeke, K., Reinhard, P.G. (eds) Time-Dependent Hartree-Fock and Beyond. Lecture Notes in Physics, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11950-7_33

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  • DOI: https://doi.org/10.1007/3-540-11950-7_33

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  • Print ISBN: 978-3-540-11950-0

  • Online ISBN: 978-3-540-39536-2

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