Distributions of the Diffusion Coefficient for the Quantum and Classical Diffusion in Disordered Media
arXiv:cond-mat/9402028
Abstract
It is shown that the distribution functions of the diffusion coefficient are very similar in the standard model of quantum diffusion in a disordered metal and in a model of classical diffusion in a disordered medium: in both cases the distribution functions have lognormal tails, their part increasing with the increase of the disorder. The similarity is based on a similar behaviour of the high-gradient operators determining the high-order cumulants. The one-loop renormalization-group corrections make the anomalous dimension of the operator that governs the -th cumulant proportional to thus overtaking for large the negative normal dimension. As behaviour of the ensemble-averaged diffusion coefficient is quite different in these models, it suggests that a possible universality in the distribution functions is independent of the behaviour of average quantities.
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