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Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations

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Zeitschrift für Physik B Condensed Matter

Abstract

General connections between the velocity autocorrelation function and the mean-square-displacement for a special initial condition are established and shown to reduce in the high-temperature limit to earlier such results obtained by Scher and Lax. A simple and useful relation, which is valid in the high temperature limit, between the velocity autocorrelation function and memory functions in generalized master equations is given.

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References

  1. Kühne, R., Reineker, P., Kenkre, V.M.: Z. Physik B (in press)

  2. Schein, L.B., Duke, C.B., McGhie, A.R.: Phys. Rev. Lett.40, 197 (1978)

    Google Scholar 

  3. Karl, N., Warta, W.: (unpublished); see also: Warta, W.: Diplomarbeit. S Stuttgart, 1978 (unpublished); Karl, N.: Abstracts of the 9th Molecular Crystal Symposium p. 149 (1980)

  4. Schein, L.B., McGhie, A.R.: Phys. Rev. B20, 1631 (1979)

    Google Scholar 

  5. Miller, A., Abrahams, E.: Phys. Rev.120, 745 (1960)

    Google Scholar 

  6. Schnakenberg, J.: Phys. Status Solidi28, 623 (1968)

    Google Scholar 

  7. Ambegaokar, V., Halperin, B.I., Langer, J.S.: Phys. Rev. B4, 2612 (1971)

    Google Scholar 

  8. Scher, H., Lax, M.: Phys. Rev. B7, 4491 (1973)

    Google Scholar 

  9. Banyai, L., Aldea, A.: Phys. Status Solidi B79, 365 (1977)

    Google Scholar 

  10. Zvyagin, I.P.: Phys. Status Solidi B85, 105 (1978)

    Google Scholar 

  11. Kubo, R.: J. Phys. Soc. Jpn.12, 570 (1957)

    Google Scholar 

  12. Karl, N.: Adv. Solid State Phys.14, 261 (1974)

    Google Scholar 

  13. Schein, L.B.: Chem. Phys. Lett.48, 571 (1977)

    Google Scholar 

  14. Holstein, T.: Ann. Phys. (N.Y.)8, 325 (1959);8, 343 (1959)

    Google Scholar 

  15. Sewell, G.L.: Phys. Rev.129, 597 (1963)

    Google Scholar 

  16. Munn, R.W., Siebrand, W.: J. Chem. Phys.52, 6391 (1970)

    Google Scholar 

  17. Emin, D.: Ann. Phys. (N.Y.)53, 439 (1969)

    Google Scholar 

  18. Madhukar, A., Post, W.: Phys. Rev. Lett.39, 1424 (1977);40, 70(E) (1978)

    Google Scholar 

  19. Munn, R.W., Silbey, R.: J. Chem. Phys.68, 2439 (1978)

    Google Scholar 

  20. Sumi, H.: Solid State Commun.28, 309 (1978);29, 495 (1979); J. Chem. Phys.70, 3775 (1979)

    Google Scholar 

  21. Efrima, S., Metiu, H.: Chem. Phys. Lett.60, 226 (1979)

    Google Scholar 

  22. Silbey, R., Munn, R.W.: J. Chem. Phys.72, 2763 (1980)

    Google Scholar 

  23. For the present context see: Kenkre, V.M.: In: Statistical mechanics and statistical methods in theory and application. Landman, U. (ed.). New York: Plenum Press 1977

    Google Scholar 

  24. Nakajima, S.: Prog. Theor. Phys.20, 948 (1958)

    Google Scholar 

  25. Zwanzig, R.: J. Chem. Phys.33, 1338 (1960)

    Google Scholar 

  26. Kenkre, V.M.: Phys. Lett.63A, 367 (1977); Phys. Rev. B18, 4064 (1978)

    Google Scholar 

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Kenkre, V.M., Kühne, R. & Reineker, P. Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations. Z. Physik B - Condensed Matter 41, 177–180 (1981). https://doi.org/10.1007/BF01293416

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  • DOI: https://doi.org/10.1007/BF01293416

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