Reply to Comment on "Exact analytic solution for the generalized Lyapunov exponent of the 2-dimensional Anderson localization"

TL;DR

This paper defends the authors' approach to analyzing 2D Anderson localization, emphasizing the importance of physical assumptions and discussing the limitations of transfer matrix methods in multi-dimensional cases.

Contribution

It clarifies the differences in physical assumptions underlying various mathematical approaches to Anderson localization and discusses transfer matrix limitations.

Findings

Different physical assumptions lead to different mathematical formalism outcomes.

Transfer matrix techniques have limitations in multi-dimensional Anderson localization.

The approach can detect co-existing pure phases in the system.

Abstract

We reply to comments by P.Marko$\breve{s}$, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect \emph{a priori} to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.