Microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size

TL;DR

This paper derives self-consistent equations for Anderson localization in finite disordered media, revealing a position-dependent diffusion coefficient influenced by the medium's boundaries.

Contribution

It provides a microscopic derivation of localization equations accounting for finite size effects and boundary-induced position dependence.

Findings

Derivation of position-dependent diffusion coefficient.

Identification of boundary effects on localization.

Establishment of self-consistent equations for finite media.

Abstract

We present a microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size. The derivation leads to a renormalized, position-dependent diffusion coefficient. The position dependence of the latter is due to the position dependence of return probability in a bounded medium.