Geodesic
The~coherent potential method in the~diffusion problem on a~random substitution lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 252-261

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Based on the balance equation, we consider the diffusion problem on a hyperlattice with randomly distributed inaccessible sites. Using diagram methods, we find a self-consistent expression for the configurationally averaged Green's function in the coherent potential approximation. We show that this approach is applicable in a broad range of concentrations of accessible sites. Using this approximation, we find the exact asymptotic form of the static diffusion coefficient for a low concentration of blocked sites. This allows making good estimates of the percolation threshold in the random-site diffusion problem on an arbitrary hyperlattice.
Keywords: coherent potential method, Green's function, percolation, random site problem, diagram method.
Mots-clés : diffusion 
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     author = {M. P. Fateev},
     title = {The~coherent potential method in the~diffusion problem on a~random substitution lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {252--261},
     publisher = {mathdoc},
     volume = {149},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a6/}
}
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M. P. Fateev. The~coherent potential method in the~diffusion problem on a~random substitution lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 2, pp. 252-261. http://geodesic.mathdoc.fr/item/TMF_2006_149_2_a6/