Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction
Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction
复制标题
二元非皮索膨胀的几何特性和绝对连续衍射的缺失
DOI：
10.4064/sm170613-10-3
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发表时间：
2017
影响因子：
0.8
通讯作者：
Jr.
中科院分区：
文献类型：
--
作者：
M. Baake;N. Frank;U. Grimm;E. Robinson;Jr.
最简单的非皮索替换规则之一在其几何版本中进行了研究，作为以自然长度间隔作为原型的平铺。通过对相关函数的详细重整化分析，我们表明衍射测量不能包含任何绝对连续的分量。这意味着除了原点处的微不足道的布拉格峰之外，衍射是纯粹奇异连续的。在此过程中，我们得出了底层 Delone 动力系统的各种几何和代数性质，我们希望这些性质也与其他此类系统相关。
One of the simplest non-Pisot substitution rules is investigated in its geometric version as a tiling with intervals of natural length as prototiles. Via a detailed renormalisation analysis of the pair correlation functions, we show that the diffraction measure cannot comprise any absolutely continuous component. This implies that the diffraction, apart from a trivial Bragg peak at the origin, is purely singular continuous. En route, we derive various geometric and algebraic properties of the underlying Delone dynamical system, which we expect to be relevant in other such systems as well.