Reply to arXiv:0709.2619 "Comment on 'Scaling behavior of classical wave transport in mesoscopic media at the localization transition' [arXiv:cond-mat/0509381]"

TL;DR

This paper critiques a previous comment on wave transport scaling laws at the localization transition, arguing that the evidence does not conclusively support a specific scaling law and calling for further calculations with larger system sizes.

Contribution

It provides a detailed rebuttal to prior claims, emphasizing the need for more extensive data to determine the correct scaling behavior at the mobility edge.

Findings

Current evidence is insufficient to confirm the T rac14; 1/L^2 scaling law.

Some data suggest a possible T rac14; ln L / L^2 behavior.

Further calculations with larger system sizes are needed.

Abstract

We argue from both technical and physical points of view that the main result shown in the Comment [arXiv:0709.2619] by Cherrolet et al. [Phys. Rev. B 80, 037101 (2009)] as well as the authors' interpretations of the result are not sufficient to draw the conclusion that the scaling law at the mobility edge takes the form T \propto 1/L^2. On the other hand, we believe that the result shows some evidence of T \propto ln L/L^2 behavior found in S. K. Cheung and Z. Q. Zhang, Phys. Rev. B 72, 235102 (2005) [arXiv:cond-mat/0509381]. More calculations with even larger L's are necessary to give a more definitive answer to this question.