Diffusion Poles and the Anderson Transition

TL;DR

This paper critiques recent theories on diffusion poles in the Anderson transition, clarifies the correct framework, and discusses the relationship between diffusion coefficients and wave function multifractality.

Contribution

It provides a corrected perspective on diffusion poles in Anderson transition theory and clarifies misconceptions from recent literature.

Findings

Recent theories are misleading and contradict principles

Correct framework for diffusion poles is established

Relationship between diffusion coefficient and multifractality is analyzed

Abstract

In the recent series of papers (cond-mat/0402471, cond-mat/0403618, cond-mat/0407618, cond-mat/0501586), Janis and Kolorenc discussed the role of the diffision poles in the Anderson transition theory. Their picture contradicts the general principles and is shown below to be completely misleading. Correct setting of the problem is given and the contemporary situation is discussed. The critical remarks are given on the relation of the diffusion coefficient with multifractality of the wave functions.