论文标题
准晶体的过度均匀性和不均匀性
Hyperuniformity and non-hyperuniformity of quasicrystals
论文作者
论文摘要
我们开发一个一般框架来研究准晶体的各种数学模型的超均匀性。使用此框架，我们提供了与以前的示例不同的非横晶准晶体的示例，不是极限句子。其中一些示例甚至是抗骨状的，或具有渐近差异差异。另一方面，我们为任意维度的欧几里得空间中的一大批数学准晶体建立了超均匀性。对于某些准晶模型，我们确定超均匀度可用于对基础参数的一般选择。对于由剪切和项目产生的准晶体，我们得出的结论是，它们的超均匀性取决于基础晶格和窗户的微妙双苯胺特性，绝不是自动的。
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.
