{
  "id": "1612.01975",
  "version": "v1",
  "published": "2016-12-06T20:09:03.000Z",
  "updated": "2016-12-06T20:09:03.000Z",
  "title": "Hyperuniformity of Quasicrystals",
  "authors": [
    "Erdal C. Oğuz",
    "Joshua E. S. Socolar",
    "Paul J. Steinhardt",
    "Salvatore Torquato"
  ],
  "comment": "12 pages, 14 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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. We employ a new criterion for hyperuniformity to quantitatively characterize quasicrystalline point sets generated by projection methods. Reciprocal space scaling exponents characterizing the hyperuniformity of one-dimensional quasicrystals are computed and shown to be consistent with independent calculations of the scaling exponent characterizing the variance $\\sigma^2(R)$ in the number of points contained in an interval of length $2R$. One-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope $1/\\tau$ are shown to fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, $\\sigma^2(R)$ is uniformly bounded for large $R$; for all others, $\\sigma^2(R)$ scales like $\\ln R$. This distinction provides a new classification of one-dimensional quasicrystalline systems and suggests that measures of hyperuniformity may define new classes of quasicrystals in higher dimensions as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-06T20:09:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperuniformity",
      "space scaling exponents characterizing",
      "one-dimensional quasicrystals",
      "quantitatively characterize quasicrystalline point sets",
      "one-dimensional quasicrystalline systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}