Anomalous diffusion and conductivity in octagonal tiling models.

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.