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Subwavelength Localisation in Nonreciprocal Disordered Systems

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

(Report number 2025-21)

Abstract
We investigate the competing mechanisms of localisation in one-dimensional disordered block subwavelength resonator systems subject to nonreciprocal damping, induced by an imaginary gauge potential. Using a symmetrisation approach to enable the adaptation of tools from Hermitian systems, we derive the limiting spectral distribution of these systems as the number of blocks goes to infinity and characterise their spectral properties in terms of the spectral properties of their constituent blocks. By employing a transfer matrix approach, we then clarify, in terms of Lyapunov exponents, the competition between the edge localisation due to imaginary gauge potentials and the bulk localisation due to disorder. In particular, we demonstrate how the disorder acts as insulation, preventing edge localisation for small imaginary gauge potentials.

Keywords: Non-Hermitian disordered system, imaginary gauge potential, random block system, subwavelength regime, edge localisation, bulk localisation, hybridisation, ergodicity, Jacobi matrices and operators

@Techreport{ABTU25_1142,
  author = {H. Ammari and S. Barandun and C. Thalhammer and A. Uhlmann},
  title = {Subwavelength Localisation in Nonreciprocal Disordered Systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-21.pdf },
  year = {2025}
}

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