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Applications of Chebyshev polynomials and Toeplitz theory to topologicalmetamaterials

by H. Ammari and S. Barandun and P. Liu

(Report number 2024-29)

Abstract
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.

Keywords: Topological metamaterials, nonreciprocal metamaterials, topological interface modes, non-Hermitian skin effect, tunable localisation, generalised Brillouin zone, Chebyshev polynomials, Toeplitz theory.

@Techreport{ABL24_1111,
  author = {H. Ammari and S. Barandun and P. Liu},
  title = {Applications of Chebyshev polynomials and Toeplitz theory to topologicalmetamaterials},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-29},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-29.pdf },
  year = {2024}
}

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