Abstract
We derive a new approach for the stochastic transport in random systems, starting from a phenomenological master equation with random transition rates. Our method combines the effective medium approximation with age-dependent dynamics. Within the framework of our approximation, the static disorder may be described by means of a system of age-dependent master equations. For translationally invariant systems which obey certain separability conditions, the approach is equivalent with the continuous time random walk theory. Moreover, for self-avoiding random walks our effective medium approximation is exact. For non self-avoiding random walks, the approximation neglects the correlations between successive transitions leading to closed paths on the lattice.
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Alexander, S., Bernasconi, J., Schneider, W.R., Orbach, R.: Rev. Mod. Phys.53, 175 (1981)
Haus, J.W., Kehr, K.W.: Phys. Rep.150, 263 (1987)
Nieuwenhuizen, Th.M., Ernst, M.H.: Phys. Rev.31B, 3518 (1985)
Ronis, D.: Phys. Rev.36A, 1908 (1987)
Summerfield, S.: Solid State Commun.39, 401 (1981)
Webman, I.: Phys. Rev. Lett.47, 1496 (1981)
Odagaki, T., Lax, M.: Phys. Rev.24B, 5284 (1981)
Machta, J.: Phys. Rev.24B, 5260 (1981)
Sahimi, Hughes, B.D., Scriven, L.E., Davis, H.T.: J. Chem. Phys.78, 6849 (1983)
Sahimi, M., Hughes, B.D., Scriven, L.E., Davis, H.T.: Phys. Rev.28B, 307 (1983)
Hughes, B.D., Sahimi, M., Scriven, L.E., Davis, H.T.: Int. J. Eng. Sci.22, 1083 (1984)
Haus, J.W., Kehr, K.W., Kitahara, K.Z.: Phys. Rev.25B, 4918 (1982)
Haus, J.W., Kehr, K.W.: Phys. Rev.36B, 5639 (1987)
Vlad, M.O., Popa, V.T., Segal, E.: Phys. Lett.100A, 387 (1984)
Vlad, M.O., Popa, V.T.: J. Phys. A.19, 45 (1986)
Vlad, M.O., Popa, V.T.: Physica142A, 579 (1987)
Vlad, M.O.: J. Phys. A20, 3367 (1987)
Montroll, E.W., West, B.J.: In: Fluctuation phenomena, Montroll, E.W., Lebowitz, J.L. (eds.), p. 93. Amsterdam: North-Holland 1979
Shlesinger, M.F.: J. Stat. Phys.10, 421 (1974)
Klafter, J., Silbey, R.: J. Chem. Phys.72, 843 (1980)
Hiller, B., Blin, A.H., Dworzecka, M., Griffin, J.J.: Nucl. Phys.424A, 335 (1984)
Gökmen, A., Dworzecka, M., Griffin, J.J.: Nucl. Phys.440A, 586 (1985)
Cugnon, J.: Z. Phys. A-Atomic Nuclei327, 187 (1987)
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Vlad, M.O., Pop, A. An age-dependent approach to random walks on disordered lattices. Z. Physik B - Condensed Matter 75, 413–420 (1989). https://doi.org/10.1007/BF01321828
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DOI: https://doi.org/10.1007/BF01321828