Length scale dependent diffusion in the Anderson model at high temperatures

TL;DR

This study examines how a single particle diffuses in a 3D disordered lattice at high temperatures, revealing that diffusion occurs only within a limited wavelength range despite strong disorder.

Contribution

It applies the TCL projection operator technique to analyze diffusion in the 3D Anderson model at high temperatures, providing detailed insights into wavelength-dependent diffusion behavior.

Findings

Diffusive dynamics occur within a limited wavelength range.

Diffusion persists even at maximal disorder for that range.

Numerical solutions support the analytical results.

Abstract

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion equation. Our approach is based on the time-convolutionless (TCL) projection operator technique and allows for a detailed investigation of this question at high temperatures. It turns out that diffusive dynamics is to be expected for a rather short range of wavelengths, even if the amount of disorder is tuned to maximize this range. Our results are partially counterchecked by the numerical solution of the full time-dependent Schroedinger equation.