Optical response of electrons in a random potential

TL;DR

This paper employs a Chebyshev expansion method to numerically analyze the AC conductivity of the Anderson model on large 3D clusters, examining boundary effects and validating the DC limit through conductance comparisons.

Contribution

It introduces a Chebyshev expansion technique for finite-temperature dynamical correlations in large-scale Anderson models, providing new insights into boundary condition effects and DC conductance validation.

Findings

Boundary conditions significantly influence AC conductivity results.

The Chebyshev method effectively computes dynamical correlations on large clusters.

Consistency between AC conductivity and conductance calculations is confirmed.

Abstract

Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity $\sigma(\omega)$ of the Anderson model on large cubic clusters of up to $100^3$ sites. Extending previous results we focus on the role of the boundary conditions and check the consistency of the DC limit, $\omega\to 0$, by comparing with direct conductance calculations based on a Greens function approach in a Landauer B\"uttiker type setup.