Comment on "Scaling behavior of classical wave transport in mesoscopic media at the localization transition"

TL;DR

This paper critiques a previous study on wave transport at the localization transition, emphasizing the importance of correctly accounting for the position-dependent diffusion coefficient to obtain accurate scaling laws.

Contribution

It clarifies the proper treatment of the position dependence of the diffusion coefficient D(r) in the self-consistent theory of localization.

Findings

The scaling law T ~ 1/L^2 is correct when D(r) is properly treated.

The previously reported T ~ ln(L)/L^2 is an artifact of an approximation.

Proper modeling of D(r) is crucial for accurate predictions at the localization transition.

Abstract

We emphasize the importance of the position dependence of the diffusion coefficient D(r) in the self-consistent theory of localization and argue that the scaling law T ~ ln(L)/L^2 obtained by Cheung and Zhang [Phys. Rev. B 72, 235102 (2005)] for the average transmission coefficient T of a disordered slab of thickness L at the localization transition is an artifact of replacing D(r) by its harmonic mean. The correct scaling T ~ 1/L^2 is obtained by properly treating the position dependence of D(r).