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J Phys Condens Matter. 2017 May 24;29(20):204003. doi: 10.1088/1361-648X/aa6944. Epub 2017 Mar 27.

Hyperuniformity variation with quasicrystal local isomorphism class.

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Department of Physics, Princeton University, Princeton, NJ 08544, United States of America.


Hyperuniformity is the suppression of long-wavelength density fluctuations, relative to typical structurally disordered systems. In this paper, we examine how the degree of hyperuniformity [[Formula: see text]] in quasicrystals depends on the local isomorphism class. By studying the continuum of pentagonal quasicrystal tilings obtained by direct projection from a five-dimensional hypercubic lattice, we find that [Formula: see text] is dominantly determined by the local distribution of vertex environments (e.g. as measured by Voronoi cells) but also exhibits a non-negligible dependence on the restorability. We show that the highest degree of hyperuniformity [smallest [Formula: see text]] corresponds to the Penrose local isomorphism class. The difference in the degree of hyperuniformity is expected to affect physical characteristics, such as transport properties.


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