From Anderson Localization to Mesoscopic Physics

TL;DR

This paper reviews the development of mesoscopic physics from Anderson localization, focusing on electron transport phenomena described by the scattering matrix, emphasizing the role of amplitude and phase in conductance.

Contribution

It provides a comprehensive overview of how scattering matrix formalism elucidates mesoscopic electron transport and interference effects, connecting localization theory to mesoscopic phenomena.

Findings

Scattering matrix formalism is key to understanding mesoscopic conductance.

Interference effects depend on both amplitude and phase of scattering matrix elements.

The review links Anderson localization concepts to observable mesoscopic phenomena.

Abstract

In the late seventies an increasing interest in the scaling theory of Anderson localization led to new efforts to understand the conductance of systems which scatter electrons elastically. The conductance and its relation to the scattering matrix emerged as an important subject. This, coupled with the desire to find explicit manifestations of single electron interference led to the emergence of mesoscopic physics. We review electron transport phenomena which can be expressed elegantly in terms of the scattering matrix. Of particular interest are phenomena which depend not only on transmission probabilities but on both amplitude and phase of scattering matrix elements.