Modulated crystals and almost periodic measures
Dynamical Systems
2024-09-05 v2 Mathematical Physics
math.MP
Abstract
Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similarly to de Bruijn's analysis, we find stability with respect to almost periodic modulations.
Keywords
Cite
@article{arxiv.1907.07017,
title = {Modulated crystals and almost periodic measures},
author = {Jeong-Yup Lee and Daniel Lenz and Christoph Richard and Bernd Sing and Nicolae Strungaru},
journal= {arXiv preprint arXiv:1907.07017},
year = {2024}
}
Comments
33 pages, 1 figure, v2: appendix shortened and restructured, other minor changes