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Applications of Chebyshev polynomials and Toeplitz theory to topological metamaterials

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arxiv 2409.18144 v1 pith:SV276Q5H submitted 2024-09-23 math-ph cond-mat.mtrl-scimath.MP

Habib Ammari , Silvio Barandun , Ping Liu This is my paper · ORCID
classification math-phcond-mat.mtrl-scimath.MP
keywords metamaterialschebyshevpolynomialstheorytoeplitztopologicalapplicationsconsider
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We survey the use of Chebyshev polynomials and Toeplitz theory for studying topological metamaterials. We consider both Hermitian and non-Hermitian systems of subwavelength resonators and provide a mathematical framework to explain some spectacular properties of metamaterials.

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  1. Bulk-edge correspondence in finite photonic structure

    math-ph 2025-01 conditional novelty 6.0 of 10

    For finite 2D photonic structures, the per-area edge circulation index converges to the bulk gap Chern number as the domain grows, conditional on unproved Green function bounds.

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