Which distributions of matter diffract? - Some answers
M. Baake, R.V. Moody, C. Richard, and B. Sing

TL;DR
This review explores which matter distributions produce pure point diffraction spectra, discussing mathematical conditions, model sets, lattice systems, and stochastic point sets, with examples like the paperfolding sequence.
Contribution
It provides a comprehensive overview of conditions for pure point diffraction and connects mathematical frameworks with specific models and stochastic systems.
Findings
Cut and project schemes explain pure point diffraction
Model sets and lattice substitution systems often yield pure point spectra
Stochastic point sets have diverse diffraction properties
Abstract
This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cut and project scheme naturally appears in this context and then turn our attention to the special situation of model sets and lattice substitution systems. As an example, we analyse the paperfolding sequence. In the last part, we summarize some aspects of stochastic point sets, with focus both on structure and diffraction.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuasicrystal Structures and Properties · Nanocluster Synthesis and Applications
