Nearly constant loss - the 2nd universality of AC conductivity by scaling down subsequent random walk steps by 1/t^(1/2)

TL;DR

This paper introduces a novel random walk model with scaled displacements to explain the nearly constant loss in AC conductivity, revealing a second universality related to anomalous diffusion characterized by logarithmic mean square displacement.

Contribution

It proposes a new random walk algorithm with displacement scaling to account for the second universality of AC conductivity in anomalous diffusion.

Findings

The model reproduces the nearly constant loss behavior in conductivity.

It demonstrates a second universality in AC conductivity related to logarithmic diffusion.

The approach links microscopic random walk dynamics to macroscopic electrical properties.

Abstract

In the frequency domain, the nearly constant loss, is characterized by a slope 1 in log of the real part of the electrical conductivity vs log frequency plots. It can be explained by an anomalous diffusion, defined by a random walk with the mean square displacement proportional to the logarithm of time, rather than being linearly proportional to time, as in normal diffusion. The present work suggests a random walk algorithm that leads to anomalous, logarithmic time dependence. That has been accomplished by scaling down the subsequent random walk displacements by a factor, 1/t^(1/2)