Anomalous Diffusion at the Anderson Transitions

Abstract

Diffusion of electrons in three-dimensional disordered systems is investigated numerically for all three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet 〈r2(t)〉 at the Anderson transition is shown to behave as ∼ta (a ≈ 2/3) From the temporal autocorrelation function C(t), the fractal dimension D2 is deduced, which is almost half the value of the space dimension for all of the universality classes.