Mesoscopic Fluctuations in Models of Classical and Quantum Diffusion

TL;DR

This paper compares mesoscopic fluctuations in classical and quantum diffusion models with long-range disorder, revealing similarities in fluctuation characteristics despite differences in average diffusion behavior, suggesting potential universality in their distribution functions.

Contribution

It demonstrates that mesoscopic fluctuation properties are similar in classical and quantum diffusion models, independent of their differing average diffusion behaviors.

Findings

Fluctuation characteristics are similar in both models in the weak-disorder limit.

Variance and higher moments relate through a weak-disorder parameter substitution.

Mesoscopic properties may be universal despite differences in average 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.