The K-theoretic bulk-boundary principle for dynamically patterned resonators

Starting from a dynamical system (Omega, G), with G a generic topological group, we devise algorithms that generate families of patterns in the Euclidean space, which densely embed G and on which G acts continuously by rigid shifts. We refer to such patterns as being dynamically generated. For G = Z(d), we adopt Bellissard's C*-algebraic formalism to analyze the dynamics of coupled resonators arranged in dynamically generated point patterns. We then use the standard connecting maps of K-theory to derive precise conditions that assure the existence of topological boundary modes when a sample is halved. We supply four examples for which the calculations can be carried explicitly. The predictions are supported by many numerical experiments. (C) 2018 Elsevier B.V. All rights reserved.