Absence of diffusion in certain random lattices: Numerical evidence

TL;DR

This paper provides numerical evidence that disorder in certain two-dimensional lattices causes electron localization, preventing diffusion and confirming quantum wave effects as the underlying mechanism.

Contribution

It offers the first detailed numerical demonstration of electron localization in disordered 2D lattices, supporting Anderson's theory.

Findings

Disorder prevents electron diffusion in 2D lattices.

Electron becomes spatially localized due to quantum effects.

Localization is confirmed as a purely quantum phenomenon.

Abstract

We demonstrate, by solving numerically the time-dependent Schroedinger equation, the physical character of electron localization in a disordered two-dimensional lattice. We show, in agreement with the prediction of P. W. Anderson, that the disorder prevents electron diffusion. The electron becomes spatially localized in a specific area of the system. Our numerical analysis confirms that the electron localization is a quantum effect caused by the wave character of electron propagation and has no analogy in classical mechanics.