A short guide to pure point diffraction in cut-and-project sets
Mathematical Physics
2020-04-02 v2 math.MP
Spectral Theory
Abstract
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.
Cite
@article{arxiv.1606.08831,
title = {A short guide to pure point diffraction in cut-and-project sets},
author = {Christoph Richard and Nicolae Strungaru},
journal= {arXiv preprint arXiv:1606.08831},
year = {2020}
}
Comments
25 pages, 3 figures, v2: presentation improved