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arXiv · 1206.1103

Periodizing quasicrystals: Anomalous diffusion in quasiperiodic systems

Atahualpa S. Kraemer·David P. Sanders
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Abstract

We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these systems,in which particles may travel without colliding, up to a critical obstacle radius. It provides a simple and efficient algorithm for numerical simulation of dynamics in quasiperiodic structures, as well as giving a natural notion of uniform distribution (measure) and averages. As an application, we simulate diffusion in a two-dimensional quasicrystal, finding three different regimes, in particular atypical weak super-diffusion in the presence of channels, and sub-diffusion when obstacles overlap.

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Atahualpa S. Kraemer, David P. Sanders. 2012-06-06. Periodizing quasicrystals: Anomalous diffusion in quasiperiodic systems. https://arxiv.org/abs/1206.1103

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