Comment on `Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

TL;DR

This paper critically examines a recent analytical approach to 2D Anderson localization, using transfer matrix methods to reveal discrepancies and discuss the validity of generalized Lyapunov exponents in localization studies.

Contribution

It provides a comparative analysis of transfer matrix results against previous signal theory findings, questioning the latter's conclusions on delocalized states.

Findings

Transfer matrix results disagree with signal theory predictions.

The study suggests potential issues with using generalized Lyapunov exponents.

It highlights the importance of methodological validation in localization research.

Abstract

In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalised states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy to use a generalised Lyapunov exponent for studying Anderson localisation.