# Third-order transport coefficients for localised and delocalised charged-particle transport

## TL;DR

This paper derives third-order transport coefficients for charged particles considering complex processes like trapping and recombination, extending classical transport laws with new insights into skewness and fractional effects.

## Contribution

It introduces a third-order skewness tensor for phase-space kinetic models, extending Fick's law and providing a physical interpretation of trap-induced skewness.

## Key findings

- Derived a skewness tensor for charged-particle transport.
- Extended Fick's law to include skewness and fractional effects.
- Explained negative skewness due to trapping phenomena.

## Abstract

We derive third order transport coefficients of skewness for a phase-space kinetic model that considers the processes of scattering collisions, trapping, detrapping and recombination losses. The resulting expression for the skewness tensor provides an extension to Fick's law which is in turn applied to yield a corresponding generalised advection-diffusion-skewness equation. A physical interpretation of trap-induced skewness is presented and used to describe an observed negative skewness due to traps. A relationship between skewness, diffusion, mobility and temperature is formed by analogy with Einstein's relation. Fractional transport is explored and its effects on the flux transport coefficients are also outlined.