English

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

R2 v1 2026-06-23T10:22:12.121Z