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 a in the model was changed from a, to alpha (2) at time tau (1) during the growth. When alpha (1) < alpha (2), our nerve-cell-like complex can be considered a dendritic fractal grown on a somatic fractal. On the other hand, when alpha (1) > alpha (2), 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 tau (1) decreases in a nerve-cell-like complex and when tau (1) 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. (C) 2001 Elsevier Science B.V. All rights reserved.