Anomalous diffusion at the Anderson transitions

Tomi Ohtsuki, Tohru Kawarabayashi

Published 1997-01-04Version 1

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.