Space-time dependence of the anomalous exponent of electric transport in the disorder model

TL;DR

This paper investigates how the anomalous exponent of electric transport varies with space and time in a disorder model, revealing the influence of network structure and confirming results through simulations.

Contribution

It introduces the space-time dependence of the anomalous exponent and highlights the network structure as a key factor, extending understanding beyond traditional models.

Findings

Anomalous exponent depends on the number of effective neighboring sites over time.

Transition from subdiffusive to normal transport occurs at long times.

Monte Carlo simulations confirm the theoretical predictions.

Abstract

Space-time dependence of the anomalous exponent of electric transport in the disorder model is presented. We show that the anomalous exponent depends on time, according to the time-evolution of the number of the effective neighbouring sites. Transition from subdiffusive to normal transport at long-enough time is recovered. The above result indicates that the spatial structure, specifically the network structure, of the hopping sites might be a novel element which determines the anomalous exponent. This leads to the feature that the scaling property of the electric transport to time is insensitive to other elements, such as the distance of the sites or the spatial dimension of the system. These findings are verified by means of Monte Carlo simulation. The relation of the result to the conventional knowledge of the Multiple Trapping Model is shown by deriving it as a special case of the disorder model.