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

R. Ugajin, S. Hirata and Y. Kuroki

Physica A: Statistical Mechanics and its Applications, 2000, vol. 278, issue 3, 312-326

Abstract: Anderson transition in a fractal-shaped structure is driven by running fractal dimension from two to three. We analyzed the spectral statistics of a quantum 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 to those of a Gaussian orthogonal ensemble. As the fractal dimension decreases to two, the spectral statistics become Poissonian. This indicates the onset of quantum localization in the fractal-shaped structure, so the Anderson transition takes place as the fractal dimension changes. The effects of introducing random potentials are also analyzed. When a random magnetic field affects quantum states extended over our fractal-shaped structure, the spectral statistics are similar to those of a Gaussian unitary ensemble. On the other hand, a random on-site potential encourages quantum localization in our fractal-shaped structure.

Keywords: Anderson transition; Spectral statistics; Quantum chaos; Fractal dimension (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:278:y:2000:i:3:p:312-326

DOI: 10.1016/S0378-4371(99)00601-9

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