Abstract
The random walk of a particle in two models of an ideal lattice with internal states has been studied. In the first model one vertical ladder of energy levels exists at each lattice site, in the second model different ladders of levels lead to neighboring sites. In thermal equilibrium, the mobility of the particle was found frequency-independent in the first model and frequency-dependent in the second. The continuous-time random walk (CTRW) description of both models has been investigated. The waiting-time distribution for the first case has been obtained analytically in the Laplace domain. An example for φ (t) has been calculated numerically by inverse Laplace transformation. In the second case an extension of the CTRW description to a backward jump model has been performed and the corresponding waiting-time distributions have been calculated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nozières, P., Iche, G.: J. Phys. (Paris)40, 225 (1979)
Pfister, G., Scher, H.: Adv. Phys.27, 747 (1978). In this review our models are called “trap-controlled hopping models”
Kimball, J. C., Adams, L. W.: Phys. Rev. B18, 5851 (1978)
Shlesinger, M.F.: J. Chem. Phys.70, 4813 (1979)
Tunaley, J.K.E.: Phys. Rev. Lett.33, 1037 (1974)
Lax, M., Scher, H.: Phys. Rev. Lett.39, 781 (1977)
Kehr, K. W., Haus, J.W.: Physica A93, 412 (1978)
Montroll, E.W., Weiss, G.H.: J. Math. Phys.6, 167 (1965)
Kac, M.: Am. Math. Monthly54, 369 (1947); reprinted in: Wax, N.: Selected Papers on Noise and Stochastic Processes. New York, Dover (1954)
Montroll, E.W., Shuler, K.E. In: Advances in Chemical Physics. Vol. 1, p. 361. New York: Wiley, Interscience (1958)
Weiss, G.H.: In Advances in Chemical Physics. Vol. 13, p. 1. New York: Wiley, Interscience (1967)
Iche, G., Nozières, P.: J. Phys. (Paris)37, 1313 (1976)
Tunaley, J.K.E.: J. Stat. Phys.11, 397 (1974), ibid.14, 461 (1976), ibid.15, 167 (1976)
Haus, J.W., Kehr, K.W.: Solid State Comuun.26, 753 (1978); J. Phys. Chem. Solids40, 1019 (1979)
Landman, U., Shlesinger, M.F.: Phys. Rev. B19, 6220 (1979)
Kehr, K.W., Richter, D., Swendsen, R.H.: J. Phys. F8, 433 (1978)
Landman, U., Montroll, E.W., Shlesinger, M.F.: Proc. Natl. Acad. Sci. USA74, 430 (1977); Kehr, K.W., Haus, J.W.: unpublished (1977); Landman, U., Shlesinger, M.F.: Phys. Rev. B19, 6207 (1979)
Feller, W.: An Introduction to Probability Theory and its Applications. Vol. I, p. 349ff. New York: Wiley 1968
Honig, G.: Dissertation Universität Dortmund (1978), Jül-Bericht Jül-1550 (1978); Honig, G., Hirdes, U.: (submitted to J. Comput. Appl. Math.)
Zwerger, W.: (unpublished)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zwerger, W., Kehr, K.W. On the frequency dependence of the conductivity in random walk models with internal states. Z. Physik B - Condensed Matter 40, 157–166 (1980). https://doi.org/10.1007/BF01295085
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01295085