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

Bodo Huckestein·Rochus Klesse
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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 $ (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.

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Bodo Huckestein, Rochus Klesse. 1999-07-01. Wave-packet dynamics at the mobility edge in two- and three-dimensional systems. https://doi.org/10.1103/physrevb.59.9714

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