Diffraction of a binary non-Pisot inflation tiling

13th International Conference on Quasicrystals

Baake, Michael^1,3 ; Grimm, Uwe^2,3

Fakultat für Mathematik, Universitat Bielefeld, Postfach 100131, Bielefeld

33501, Germany^1

School of Mathematics and Statistics, Open University, Milton Keynes

MK7 6AA, United Kingdom^2

School of Mathematics and Physics, University of Tasmania, Hobart

TAS

7001, Australia^3

关键词: Bragg peaks;    Diffraction spectra;    Fibonacci;    Inflation factors;    Inflation rule;    One dimension;    One parameter family;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/809/1/012026/pdf
DOI  :  10.1088/1742-6596/809/1/012026

来源: IOP

【 摘 要 】

A one-parameter family of binary inflation rules in one dimension is considered. Apart from the first member, which is the well-known Fibonacci rule, no inflation factor is a unit. We identify all cases with pure point spectrum, and discuss the diffraction spectra of other members of the family. Apart from the trivial Bragg peaks at the origin, they have purely singular continuous diffraction.