Periodizing quasicrystals: Anomalous diffusion in quasiperiodic systems

Autor:	Kraemer, Atahualpa S., Sanders, David P.
Rok vydání:	2012
Předmět:	Nonlinear Sciences - Chaotic Dynamics Condensed Matter - Materials Science Condensed Matter - Statistical Mechanics Mathematics - Dynamical Systems Physics - Computational Physics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 5 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1206.1103 Zobrazit plný text záznamu View this record from Arxiv