Analysis of a generalised Boltzmann equation for anomalous diffusion under time-dependent fields

TL;DR

This paper extends the generalized Boltzmann equation to include time-dependent fields, demonstrating how AC fields can probe trapping rates and reveal signatures of fractional anomalous diffusion in materials.

Contribution

It introduces a framework for analyzing anomalous diffusion under AC fields using a generalized Boltzmann equation, linking transport properties to experimental probing methods.

Findings

AC fields can probe trapping and detrapping rates.

Signature of fractional diffusion under AC fields identified.

Conditions for dispersive transport analyzed.

Abstract

The generalised Boltzmann equation which treats the combined localised and delocalised nature of transport present in certain materials is extended to accommodate time-dependent fields. In particular, AC fields are shown to be a means to probe the trapping and detrapping rates of materials under certain conditions. Conditions leading to dispersive transport are considered, and the signature of fractional/anomalous diffusion under AC electric fields is presented.