Weak disorder corrections of the scattering and transport mean free path

TL;DR

This paper calculates weak localisation corrections to scattering and transport mean free paths in wave propagation through a delta-correlated random potential, revealing linear dependence on disorder parameter and effects beyond diffusion approximation.

Contribution

It provides a novel calculation of weak localisation effects on both mean free paths, including corrections beyond the diffusion approximation, showing linear dependence on the disorder parameter.

Findings

Both scattering and transport mean free paths are affected by interference.

The leading order correction depends linearly on the disorder parameter 1/kl.

Contrasts with diffusion approximation results where scattering mean free path is unaffected.

Abstract

We present a calculation of the weak localisation correction to the scattering and to the transport mean free path, for waves propagating in a $delta$-correlated random potential, going beyond the usual diffusion approximation for the loops in the interfering path amplitudes. We find that not only the transport mean free path, but also the scattering mean free path is affected by the interference contributions. We also find the dependence of the leading order contribution to both, the scattering and the transport mean free path, on the disorder parameter $1/kl$ to be linear. This is in contrast to the result obtained from the diffusion approximation according to which the scattering mean free path remains unaffected when changing the disorder parameter, whereas the correction of the transport mean free path scales like $1/(kl)^2$.