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- Title
Hyperuniformity and non-hyperuniformity of quasicrystals.
- Authors
Björklund, Michael; Hartnick, Tobias
- 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.
- Subjects
QUASICRYSTALS; MATHEMATICAL models; HYPERGRAPHS
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 1, p365
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02647-1