Anderson transition driven by running fractal dimensions in a fractal-shaped structure

Anderson transition in a fractal-shaped structure is driven by running frac tal dimension from two to three. We analyzed the spectral statistics of a q uantum particle confined in a fractal-shaped structure generated using the dielectric breakdown model in three dimensions. When the fractal dimension is almost three, the spectral statistics of low-energy states are similar t o those of a Gaussian orthogonal ensemble. As the fractal dimension decreas es to two, the spectral statistics become Poissonian. This indicates the on set of quantum localization in the fractal-shaped structure, so the Anderso n transition takes place as the fractal dimension changes. The effects of i ntroducing random potentials are also analyzed. When a random magnetic fiel d affects quantum states extended over our fractal-shaped structure, the sp ectral statistics are similar to those of a Gaussian unitary ensemble. On t he other hand, a random on-site potential encourages quantum localization i n our fractal-shaped structure. (C) 2000 Elsevier Science B.V. All rights r eserved.