Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

Bodo Huckestein; Rochus Klesse

doi:10.1103/PhysRevB.59.9714

paper

Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

arXiv:cond-mat/9805038 · doi:10.1103/PhysRevB.59.9714

Abstract

We study the time evolution of wave packets at the mobility edge of disordered non-interacting 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 $k$ -th moment of the probability density $< r^{k} > (t)$ scales like $t^{k / d}$ in $d$ dimensions. The return probability $P (r = 0, t)$ scales like $t^{- D_{2} / d}$ , 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 $P (r, t) \propto t^{- D_{2} / d} r^{D_{2} - d}$ . 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.

4 pages, RevTeX, 4 figures included, published version

Wave-packet dynamics at the mobility edge in two- and three-dimensional systems

Abstract

References in corpus (5)

Cited by in corpus (27)