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Hyperuniformity of quasicrystals

Author(s): Oguz, Erdal C; Socolar, Joshua ES; Steinhardt, Paul J.; Torquato, Salvatore

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Abstract: Hyperuniform systems, which include crystals, quasicrystals, and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity Z(k) to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of Z(k) as k tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, sigma(2)(R), in the number of points contained in an interval of length 2R. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope 1/tau fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, Z(k) similar to k(4); for all others, Z(k) similar to k(2). This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.
Publication Date: 1-Feb-2017
Electronic Publication Date: 23-Feb-2017
Citation: Oguz, Erdal C, Socolar, Joshua ES, Steinhardt, Paul J, Torquato, Salvatore. (2017). Hyperuniformity of quasicrystals. PHYSICAL REVIEW B, 95 (10.1103/PhysRevB.95.054119
DOI: doi:10.1103/PhysRevB.95.054119
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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