Mesoscopic Fluctuations in Models of Classical and Quantum Diffusion

Abstract

It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the weak-disorder limit. The relative values of the variance and of the high-order moments of the fluctuations in one model are obtained from those in another one by substituting a proper weak-disorder parameter. As behaviour of the ensemble-averaged diffusion coefficient is quite different in these models, it suggests that the mesoscopic properties, including a possible universality in the distribution functions, could be independent of the behaviour of the averaged quantities.