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Single-ion random walk on a lattice in an attractive coulomb cutoff potential

  • R. Kutner
  • D. Knödler
  • P. Pendzig
  • R. Przeniosło
  • W. Dieterich
Invited Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 438)

Keywords

Random Walk Solid State Ionic Coulomb Potential Inverse Temperature Smoluchowski 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.

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References

  1. [1]
    Funke, K.: Jump' relaxation in solid electrolytes. Progr. Solid State Chem. 22 (1993) 251–341Google Scholar
  2. [2]
    Rackovsky, S., Scher, H.: Theory of geminate recombination on a lattice. IV. Results using large Coulomb radii on the simple cubic and square lattices. J. Chem. Phys. 89 (1988) 7242–7252Google Scholar
  3. [3]
    Calef, D.F., Deutch, J.M.: Diffusion-controlled reactions. Annu. Rev. Phys. Chem. 34 (1983) 493–524Google Scholar
  4. [4]
    Rice, S.A.: Diffusion-limited reactions. (Elsevier, Amsterdam, 1985)Google Scholar
  5. [5]
    Ovchinnikov, A.A., Timashev, S.F., Bely, A.A.: Kinetika Diffusion no-kontroliruemyh Kimicheskih Processov. (Kimija, Moscow, 1986)Google Scholar
  6. [6]
    Schwarzer, S., Havlin, S., Stanley, E.H.: Multifractal scaling of 3d diffusion-limited aggregation. Physica A 191 (1992) 117–122Google Scholar
  7. [7]
    Coniglio, A.: Is diffusion limited aggregation scale invariant? Physica A 200 (1993) 165–170Google Scholar
  8. [8]
    Kehr, K.W., Binder, K.: Simulation of diffusion in lattice gases and related kinetic phenomena. Topics in Current Physics. Vol. 36: Applications of the Monte Carlo Method in Statistical Physics. Ed. Binder, K. (Springer, Berlin, 1984) Chap.6, p.181–221Google Scholar
  9. [9]
    Taitelbaum, H.: Segregation in reaction-diffusion systems. Physica A 200 (1993) 155–164Google Scholar
  10. [10]
    Aslangul, C., Pottier, N., Chvosta, P., Saint-James, D., Skala, L.: Randomrandom walk on an asymmetric chain with a trapping attractive center. J. Stat. Phys. 69 (1992) 17–34Google Scholar
  11. [11]
    Onsager, L.: Initial recombination of ions. Phys. Rev. 54 (1938) 554–557Google Scholar
  12. [12]
    Hong, K.M., Noolandi, J.: Solution of the time-dependent Onsager problem. J. Chem. Phys. 68 (1978a) 5026–5039Google Scholar
  13. [12a]
    Hong, K.M., Noolandi, J.: Solution of the Smoluchowski equation with a Coulomb potential. I. General results. J. Chem. Phys. 68 (1978b) 5Google Scholar
  14. [12b]
    Hong, K.M., Noolandi, J.: Solution of the Smoluchowski equation with a Coulomb potential. II. Application to fluorescence quenching. J. Chem. 68 (1978c) 5172–5176Google Scholar
  15. [13]
    Traytak, S.D.: On the solution of the Debye-Smoluchowski equation with a Coulomb potential. I. The case of a random initial distribution and a perfectly absorbing sink. Chem. Phys. 140 (1990) 281–297Google Scholar
  16. [13a]
    Traytak, S.D.: On the solution of the Debye-Smoluchowski equation with a Coulomb potential. II. An approximation of the time-dependent rate constant. Chem. Phys. 150 (1991a) 1–12Google Scholar
  17. [13b]
    Traytak, S.D.: On the solution of the Debye-Smoluchowski equation with a Coulomb potential. III. The case of a Boltzmann initial distribution and a perfectly absorbing sink. Chem. Phys. 154 (1991b) 263–280Google Scholar
  18. [14]
    Pedersen, J.B., Lolle, L.I., Jorgensen, J.S.: An optimal numerical solution of diffusional recombination problems. Chem. Phys. 165 (1992) 339–349Google Scholar
  19. [15]
    Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7 (1940) 284–304Google Scholar
  20. [16]
    Hänggi, P., Talkner, P., Borkovec, M.: Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62 (1990) 251–341Google Scholar
  21. [17]
    Risken, H.: The Fokker-Planck Equation. Methods of Solution and Applications. 2. Edition (Springer, 1989)Google Scholar
  22. [18]
    Knödler, D., Dieterich, W.: Lattice-gas models of dispersive transport in disordered materials. Physica A 191 (1992) 426–432Google Scholar
  23. [19]
    Petersen, J., Dieterich, W.: Effects of Coulomb interaction and disordered in a stochastic lattice gas. Phil. Mag. B 65 (1992) 231–241Google Scholar
  24. [20]
    Maass, P., Petersen, J., Bunde, A., Dieterich, W., Roman, H.E.: Non-Debye relaxation in structurally disordered ionic conductors: effect of Coulomb interaction. Phys. Rev. Lett., 66 (1991) 52–55Google Scholar
  25. [21]
    Nitzan, A., Druger, S.D., Ratner, M.A.: Random walk in dynamically disordered systems. Phil. Mag. B 56 (1987) 853–859Google Scholar
  26. [22]
    Ratner, M.A., Nitzan, A.: Fast ion conduction: some theoretical issues. Solid State Ionics'87. Proceed. 6th Intern. Conf. Solid State Ionics'87. Eds. Weppner, W., Schutz, H. (Garmisch-Partenkirchen, 1987) p.3–33Google Scholar
  27. [23]
    Bunde, A.: Anomalous transport in disordered media. Solid State Ionics'87. Proceed. 6th Intern. Conf. Solid State Ionics. Eds. Weppner, W., Schulz, H. (Garmisch-Partenkirchen, 1987) p.34–40Google Scholar
  28. [24]
    Dieterich, W.: Transport in ionic solids: Theoretical aspects. High conductivity solid ionic conductors-recent trends and applications. (World Scientific, Singapore, 1989) p.17–44Google Scholar
  29. [25]
    Binder, K.: Introduction: Theory and “technical” aspects of Monte Carlo simulations. Topics in Current Physics. Vol. 7: Monte Carlo Methods in Statistical Physics. Ed. Binder, K. (Springer, Berlin, 1979) Chap. 1, p.1–45Google Scholar
  30. [26]
    Majid, I., Ben-Avraham, D., Havlin, S., Stanley, H.E.: Exact-enumeration approach to random walks on percolation clusters in two dimensions. Phys. Rev. B 30 (1984) 1626–1628Google Scholar
  31. [27]
    Havlin, S., Ben-Avraham, D.: Diffusion in disordered media. Adv. Phys. 36 (1987) 695–798Google Scholar
  32. [28]
    Bunde, A., Dieterich, W.: Dynamic correlations in charged lattice gas. Phys. Rev. B 31 (1985) 6012–6021Google Scholar
  33. [29]
    Dieterich, W., Peschel, I., Schneider, W.R.: Diffusion in periodic potentials. Z. Physik B 27 (1977) 177–187Google Scholar
  34. [30]
    Allegrini, M., Arimondo, E., Bambini, A.: Matrix continued-fraction solution for saturation effects in spin-1/2 radio-frequency spectroscopy spectroscopy. Phys. Rev. A 15 (1977) 718–726Google Scholar
  35. [31]
    Zwerger, W., Kehr, K.W.: On the frequency dependence of the conductivity in random walk models with internal states. Z. Physik B-Cond. Matt. 40 (1980) 157–166Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • R. Kutner
    • 1
  • D. Knödler
    • 1
  • P. Pendzig
    • 1
  • R. Przeniosło
    • 2
  • W. Dieterich
    • 1
  1. 1.Fakultät für PhysikKonstanzGermany
  2. 2.Department of PhysicsWarsaw UniversityWarsawPoland

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