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Truncated Floquet-Bloch transform for computing the spectral properties of large finite systems of resonators

by H. Ammari and S. Barandun and A. Uhlmann

(Report number 2024-33)

Abstract
This paper aims at providing for the first time the mathematical foundations of the truncated Floquet-Bloch transform, which can be used to characterise the spectral properties of finite periodic and aperiodic large systems of resonators.

Keywords: Finite periodic structures, bandgaps, essential spectrum convergence, defect eigenmode, Toeplitz theory, Su–Schrieffer–Heeger model, aperiodic structure, dislocated chain, topological defect.

@Techreport{ABU24_1115,
  author = {H. Ammari and S. Barandun and A. Uhlmann},
  title = {Truncated Floquet-Bloch transform for computing the spectral properties of large finite systems of resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-33},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-33.pdf },
  year = {2024}
}

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