Crossover Characterization of the Spectral Statistics in Fractal-Based Complexes with Random Magnetic Fields

Abstract

A crossover distribution specified by two parameters (ω, η) is introduced to describe the transition of spectral statistics from Poissonian to the Gaussian unitary ensemble. During the transition, appropriate values of (ω, η) will move along a route from (0,0) to (1,1) in the (ω, η) plane. This difference between the route of a nerve-cell-like fractal-based complex and that of a nebula-like fractal-based complex elicits different spectral behaviors during the Anderson transition in these fractal-based complexes with random magnetic fields.