Zeitschrift für Physik B Condensed Matter

, Volume 27, Issue 2, pp 177–187

Diffusion in periodic potentials

  • W. Dieterich
  • I. Peschel
  • W. R. Schneider
Article

Abstract

We discuss the static and dynamic phenomena connected with the Brownian motion of a particle in a periodic potential. Specifically we consider the dynamic mobility and the dynamic structure factor. We show with numerical examples how translational and oscillatory motion show up in these quantities. The calculations are done for the onedimensional case. A main tool is the continued fraction expansion of the relevant correlation functions. It enables us, for example, to obtain numerically accurate results for the mobility in a cosine potential. Possible applications of this model lie in the fields of superionic conductors and molecular crystals with rotational diffusion.

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References

  1. 1.
    Zeller, H.R., Brüesch, P., Pietronero, L., Strässler, S.: Superionic Conductors (edited by Mahan, G.D., Roth, W.L.) p. 201. New York and London: Plenum Press 1976Google Scholar
  2. 2.
    For a review see Funke, K.: Progr. Solid St. Chem.11, 345 (1967)Google Scholar
  3. 3.
    Funke, K., Jost, A.: Ber. Bunsenges. Phys. Chem.75, 436 (1971)Google Scholar
  4. 4.
    Brüesch, P., Strässler, S., Zeller, H.R.: Phys. Stat. Solidi (a)31, 217 (1975)Google Scholar
  5. 5.
    Fulde, P., Pietronero, L., Schneider, W.R., Strässler, S.: Phys. Rev. Letters35, 1776 (1975)Google Scholar
  6. 6.
    Huberman, B.A., Sen, P.N.: Phys. Rev. Letters33, 1379 (1974)Google Scholar
  7. 7.
    Weiner, J.H., Froman, R.E.: Phys. Rev. B10, 315 (1974)Google Scholar
  8. 8.
    For a review see Bonzel, H.P.: International Summer Institute in Surface Science, Milwaukee (Wisconsin), 1975 (to be publiched)Google Scholar
  9. 9.
    For a review see Springer, T.: Springer Tracts in Modern Physics, Vol.64, edited by G. Höhler, Berlin-Heidelberg-New York: Springer 1972Google Scholar
  10. 10.
    Kubo, R.: Rep. Progr. Phys.29, 255 (1966)Google Scholar
  11. 11.
    Bixon, M., Zwanzig, R.: J. Stat. Phys.3, 245 (1971)Google Scholar
  12. 12.
    Kramers, H.A.: Physica7, 284 (1940)Google Scholar
  13. 13.
    Chudley, C.T., Elliott, R.J.: Proc. Phys. Soc.77, 353 (1961)Google Scholar
  14. 14.
    For a review see Kehr, K.W.: Diffusion von Wasserstoff in Metallen, Berichte der Kernforschungsanlage Jülich — Nr. 1211 (1975)Google Scholar
  15. 15.
    Eckold, G., Funke, K., Kalus, J., Lechner, R.E.: J. Phys. Chem. Solids37, 1097 (1976)Google Scholar
  16. 16.
    Wall, H.S.: Analytic Theory of Continued Fractions, p. 192. New York: Chelsea Publishing Company 1948Google Scholar
  17. 17.
    Schneider, W.R.: Z. Physik B24, 135 (1976)Google Scholar
  18. 18.
    Mori, H.: Progr, Theor. Phys.34, 399 (1965)Google Scholar
  19. 19.
    See for example Sears, V.F.: Can. J. Phys.47, 199 (1969)Google Scholar
  20. 20.
    Chandrasekhar, S.: Rev. Mod. Phys.15, 1 (1943)Google Scholar
  21. 21.
    Egelstaff, P.A.: An Introduction to the Liquid State, London, New York: Academic Press 1967Google Scholar
  22. 22.
    This equation can be derived in analogy to Ambegaokar, V., Halperin, B.I.: Phys. Rev. Letters22, 1364 (1969)Google Scholar
  23. 23.
    Morse, P.M., Feshbach, H.: Methods in Theoretical Physics, p. 884. New York: McGraw-Hill 1953Google Scholar
  24. 24.
    Continued fraction methods in connection with Schrödinger equations have been used e.g. by Scofield, D.F.: Phys. Rev. Letters29, 811 (1972), Götze, W.: Lett. Nuovo Cimento7, ser, 2, 187 (1973); see also Smith, W.A.: Phys. Rev. Letters32, 1, 1974Google Scholar
  25. 25.
    Schneider, W.R., Strässler, S.: Submitted to Z. PhysikGoogle Scholar
  26. 26.
    Gissler, W., Stump, N.: Physica65, 109 (1973)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • W. Dieterich
    • 1
  • I. Peschel
    • 1
  • W. R. Schneider
    • 2
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Federal Republic of Germany
  2. 2.Brown Boveri Research CenterBadenSwitzerland

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