Anne E. B. Nielsen: Topological quantum systems in fractals and quasicrystals
Describing quantum models on Bravais lattice structures has a long tradition in condensed matter physics. Progress in quantum engineering, however, motivates the study of non-periodic systems, where the choice of lattice structure is seen as a parameter. Here, we investigate the possibility to obtain topological models on fractals and quasicrystals. We show that anyons and the fractional quantum Hall effect can be realized in fractal dimensions between 1 and 2, and we discuss a new type of topological states in quasicrystals.
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