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Subwavelength Localisation in Disordered Systems

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

(Report number 2025-01)

Abstract
We consider disordered finite systems of subwavelength resonators where the disorder is in the spatial arrangement of the resonators and their material parameters are perturbed randomly. We elucidate the mechanism of wave localisation in such systems. To do so, we employ the capacitance matrix formalism, make precise the notions of bandgap and localised eigenmodes, study their stabilities with respect to fluctuations in the system, and highlight the importance of defect hybridisation and level repulsion in creating localised eigenmodes for a given arrangement of the resonators by randomly changing their material parameters. We also introduce a method of localised eigenmode prediction based on the discrete Green function of the disordered system of resonators and show the existence of bound eigenmodes in disordered systems where local translation invariance is broken.

Keywords: Disordered system, subwavelength localisation, delocalisation, bandgap, bound eigenmode, defect eigenmode.

@Techreport{ABU25_1122,
  author = {H. Ammari and S. Barandun and A. Uhlmann},
  title = {Subwavelength  Localisation in Disordered Systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-01.pdf },
  year = {2025}
}

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