1998/05/31 by Bodo Huckestein, Rochus Klesse · 36 citations
Mathematics · Physics and Astronomy · #Combinatorics #Dimension (graph theory) #Geometry #Mathematical physics #Mathematics #Moment (physics) #Operator (biology) #Opinion Dynamics and Social Influence #Physics #Power law #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Scaling #Second moment of area #Statistical physics #Statistics #Wave packet #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.59.9714
published in Physical review. B, Condensed matter 59(15), 9714-9717 (American Physical Society) · 4 pages, RevTeX, 4 figures included, published version
openalex publication_date 1999/04/15 · arxiv created 1999/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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-D2/d, with the generalized dimension of the participation ratio D2. For long times and short distances the probability density of the wave packet shows power-law scaling P(r,t)\ensuremath∝t^\ensuremath-D2/dr^D2\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.