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Eigenfunction Antisymmetric relation Degenerate energy levels Symmetry (geometry) Loop (graph theory) Zero (linguistics) Physics Eigenvalues and eigenvectors Simplicity Action (physics) Topology (electrical circuits) Mathematics Classical mechanics Geometry Quantum mechanics Mathematical physics Combinatorics Philosophy Linguistics

Housni Al Wahsh , L. Dobrzyński , Abdellatif Akjouj , El Houssaine El Boudouti ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.1016/b978-0-12-819388-4.00013-7 · OA: W3127773764

The simplest general robust zero is the middle of an open loop. When the middles of several free-end open loops of the same length are superposed, their antisymmetric eigenfunctions remain unperturbed and the final network has several degenerate states. The next three examples take into account spatial symmetry breaks. It is assumed for simplicity that all loops are made out of the same dielectric material. A robust eigenfunction zero is robust because its eigenstate cannot be activated by any action applied on it. The path states are robust because they are confined within one-dimensional paths and when they are degenerate they can turn around defects.