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Hyperuniformity and non-hyperuniformity of quasicrystals

Björklund, Michael; Hartnick, Tobias 1
1 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)

Abstract:

We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic. Some of these examples are even anti-hyperuniform or have a positive asymptotic number variance. On the other hand we establish hyperuniformity for a large class of mathematical quasicrystals in Euclidean spaces of arbitrary dimension. For certain models of quasicrystals we moreover establish that hyperuniformity holds for a generic choice of the underlying parameters. For quasicrystals arising from the cut-and-project method we conclude that their hyperuniformity depends on subtle diophantine properties of the underlying lattice and window and is by no means automatic.


Verlagsausgabe §
DOI: 10.5445/IR/1000160553
Veröffentlicht am 26.07.2023
Originalveröffentlichung
DOI: 10.1007/s00208-023-02647-1
Scopus
Zitationen: 3
Web of Science
Zitationen: 3
Dimensions
Zitationen: 5
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2023
Sprache Englisch
Identifikator ISSN: 0025-5831, 1432-1807
KITopen-ID: 1000160553
Erschienen in Mathematische Annalen
Verlag Springer
Vorab online veröffentlicht am 21.06.2023
Nachgewiesen in Scopus
Web of Science
Dimensions
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