Anomalous diffusion at the Anderson transitions

TL;DR

This paper numerically investigates electron diffusion at the Anderson transition across three universality classes, revealing anomalous diffusion characterized by specific temporal behaviors and fractal dimensions.

Contribution

It provides a comprehensive numerical analysis of wave packet dynamics at the Anderson transition for all three universality classes, highlighting universal anomalous diffusion properties.

Findings

Wave packet second moment scales as t^{2/3} at the transition.

Fractal dimension D_2 is approximately half the space dimension.

Universal behavior across orthogonal, unitary, and symplectic classes.

Abstract

Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $<\vv{r}^2(t)>$ at the Anderson transition is shown to behave as $\sim t^a (a\approx 2/3)$. From the temporal autocorrelation function $C(t)$, the fractal dimension $D_2$ is deduced, which is almost half the value of space dimension for all the universality classes.