Abstract
We study the time evolution of wave packets at the mobility edge of disordered noninteracting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory. In particular, we find that the return probability $P(r=0,t)$ scales like ${t}^{\ensuremath{-}{D}_{2}/d}$, with the generalized dimension of the participation ratio ${D}_{2}$. For long times and short distances the probability density of the wave packet shows power-law scaling $P(r,t)\ensuremath{\propto}{t}^{\ensuremath{-}{D}_{2}/d}{r}^{{D}_{2}\ensuremath{-}d}$. The numerical calculations were performed on network models defined by a unitary time evolution operator providing an efficient model for the study of the wave-packet dynamics.
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