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Anomalous diffusion and conductivity in octagonal tiling models

Anomalous diffusion and conductivity in octagonal tiling models We present numerical calculations of the quantum diffusion over an octagonal quasiperiodic tiling. We have studied a one-parameter family of Hamiltonians including the pure hopping case, the Laplacian, and a regime where atomic potentials prevail. We have found that unlimited diffusion occurs with anomalous exponents both in the hopping regime, where the spectrum has a band structure, and in the strong-coupling regime, where the spectrum has a Cantor structure. Upon introducing disorder in the lattice through phasonic fluctuations, the diffusion exponent increases in the pure hopping regime, while localization appears in the strong-coupling regime. The consequences on the conductivity of real quasicrystals are considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Anomalous diffusion and conductivity in octagonal tiling models

Passaro, B
Physical Review B , Volume 46 (21) – Dec 1, 1992
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1992 The American Physical Society
ISSN
1095-3795
DOI
10.1103/PhysRevB.46.13751
Publisher site
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Abstract

We present numerical calculations of the quantum diffusion over an octagonal quasiperiodic tiling. We have studied a one-parameter family of Hamiltonians including the pure hopping case, the Laplacian, and a regime where atomic potentials prevail. We have found that unlimited diffusion occurs with anomalous exponents both in the hopping regime, where the spectrum has a band structure, and in the strong-coupling regime, where the spectrum has a Cantor structure. Upon introducing disorder in the lattice through phasonic fluctuations, the diffusion exponent increases in the pure hopping regime, while localization appears in the strong-coupling regime. The consequences on the conductivity of real quasicrystals are considered.

Journal

Physical Review B – American Physical Society (APS)

Published: Dec 1, 1992

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