2022/10/05 by Michael Björklund, Björklund, Michael, Tobias Hartnick +1 · 2 citations
Materials Science · #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Probability (math.PR) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2210.02151
openalex publication_date 2022/10/05 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
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.