DISTRIBUTIONS OF THE DIFFUSION-COEFFICIENT FOR THE QUANTUM AND CLASSICAL DIFFUSION IN DISORDERED MEDIA

It is shown that the distribution functions of the diffusion coefficie nt are very similar in the standard model of quantum diffusion in a di sordered metal and in a model of classical diffusion in a disordered m edium: in both cases the distribution functions have lognormal tails, their part increasing with the increase of the disorder. The similarit y is based on a similar behaviour of the high-gradient operators deter mining the high-order cumulants. The one-loop renormalization-group co rrections make the anomalous dimension of the operator that governs th e sth cumulant proportional to s(s - 1) thus overtaking for large s th e negative normal dimension. As behaviour of the ensemble-averaged dif fusion coefficient is quite different in these models, it suggests tha t a possible universality in the distribution functions is independent of the behaviour of average quantities.