Systematic density expansion for random resistor networks

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Abstract
The authors present a systematic density expansion for calculating transport properties, return probabilities and spectral densities for lattice hopping models with diluted randomness. The method is applied to a disordered square lattice where the bonds carry conductances sigma 1 and sigma 2 in concentrations c and 1-c, respectively, and they calculate explicitly the O(c) and O(c2) contributions to the static conductivity (diffusion coefficient) and to the coefficient beta (c) of the long time tail in the velocity autocorrelation function (VACF) ( upsilon x(0) upsilon x(t)) approximately=- beta (c)t-2. To O(c) the VACF is calculated for all times and shows negative correlation (cage effect) for all times.