Classifying the Dynamics of Architected Materials by Groupoid Methods
Operator Algebras
2023-12-11 v3 Materials Science
Mathematical Physics
math.MP
Abstract
We consider synthetic materials consisting of self-coupled identical resonators carrying classical internal degrees of freedom. The architecture of such material is specified by the positions and orientations of the resonators. Our goal is to calculate the smallest C*-algebra that covers the dynamical matrices associated to a fixed architecture and adjustable internal structures. We give the answer in terms of a groupoid C*-algebra that can be canonically associated to a uniformly discrete subset of the group of isometries of the Euclidean space. Our result implies that the isomorphism classes of these C*-algebras split these architected materials into classes containing materials that are identical from the dynamical point of view.
Keywords
Cite
@article{arxiv.2308.07866,
title = {Classifying the Dynamics of Architected Materials by Groupoid Methods},
author = {Bram Mesland and Emil Prodan},
journal= {arXiv preprint arXiv:2308.07866},
year = {2023}
}