Anderson transition in fractal-based complexes

We investigated the Anderson transition in fractal-based complexes, which were generated using the dielectric-breakdown model when parameter α in the model was changed from α1 to α2 at time τ1 during the growth. When α1<α2, our nerve-cell-like complex can be considered a dendritic fractal grown on a somatic fractal. On the other hand, when α1>α2, our nebula-like complex cannot be divided into two regions. The spectral statistics of a quantum particle in these fractal-based complexes were analyzed and the result indicates the existence of an Anderson transition. An extended electron showing quantum chaos becomes localized when τ1 decreases in a nerve-cell-like complex and when τ1 increases in a nebula-like complex. It is shown that these two types of fractal-based complexes can be distinguished by the type of Anderson transition, the features of which are characterized based on the Berry–Robnik distribution.