{
  "abstract": "Quasicrystals exhibit long-range order without translational periodicity, posing challenges to compute their electronic properties. Here we show that a quasicrystal can be represented exactly as a periodic approximant with a spatially graded phason, establishing a connection to functionally graded materials. Building on this connection, we develop a controlled quantum theory of quasicrystals. We derive a state-dependent control parameter governed by the quantum metric of local Bloch states, determining when finite approximations are reliable. We further construct a Hamiltonian that correctly predicts Bragg gap positions, quasimomentum equivalence, and quasiperiodic eigenstates to all orders in phason strain within a finite Fourier window. We verify the theory numerically and propose a diffraction-based experimental test of the gap shift induced by phason strain. Our framework opens a route to predicting the electronic structure and functional properties of quasicrystals using methods developed for functionally graded materials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05478",
  "author_total": 5,
  "authors": [
    {
      "name": "Michael J. Landry"
    },
    {
      "name": "Dominic Bollettieri"
    },
    {
      "name": "Akhil Sadam"
    },
    {
      "name": "Denisse Córdova Carrizales"
    },
    {
      "name": "Mingda Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbdy5awb5fg92.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05478",
  "fulltext_url": null,
  "id": "cbdy5awb5fg92",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05478",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbdy5awb5fg92.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05478"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Quasicrystals are Functionally Graded Materials",
  "title_text": "Quasicrystals are Functionally Graded Materials",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/cbdy5awb5fg92",
  "venue": "arXiv",
  "versions": []
}