Diffusion and multifractality at the metal-insulator transition

TL;DR

This paper reviews the dynamics of wavepackets at the metal-insulator transition, emphasizing scale invariance, multifractality, and the role of network models in understanding disordered systems.

Contribution

It highlights the significance of multifractal eigenfunction fluctuations and the frequency- and wavevector-dependent diffusion coefficient at the transition.

Findings

Scale invariance and multifractality are key at the transition.

Network models effectively simulate disordered system dynamics.

Numerical simulations support the theoretical insights.

Abstract

We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of the frequency- and wavevector-dependence of the diffusion coefficient are compared with the results of numerical simulations. We argue that network models are particularly suited for the investigation of the dynamics of disordered systems.