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 sth cumulant proportional to s(s - 1) thus overtaking for large s 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.
|Number of pages||19|
|Journal||Nuclear Physics A|
|Publication status||Published - 12 Jul 1993|