Anderson Transition and Generalized Lyapunov Exponents (comment on comment by P.Markos, L.Schweitzer and M.Weyrauch, cond-mat/0402068)

TL;DR

This paper critiques recent approaches to using generalized Lyapunov exponents in Anderson transition theory, clarifying misconceptions and contrasting different methodologies in the literature.

Contribution

It provides a critical analysis of recent claims about generalized Lyapunov exponents and clarifies the correct approach in the context of Anderson transition theory.

Findings

Markos et al.'s approach is incorrect

Differences between Kuzovkov et al. and the author’s methods are discussed

Clarification of the proper use of generalized Lyapunov exponents in the theory

Abstract

The generalized Lyapunov exponents describe the growth of the second moments for a particular solution of the quasi-1D Schroedinger equation with initial conditions on the left end. Their possible application in the Anderson transition theory became recently a subject for controversy in the literature. The approach to the problem of the second moments advanced by Markos et al (cond-mat/0402068) is shown to be trivially incorrect. The difference of approaches by Kuzovkov et al (cond-mat/0212036, cond-mat/0501446) and the present author (cond-mat/0504557, cond-mat/0512708) is discussed.