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Stability of the non-Hermitian skin effect

by H. Ammari and S. Barandun and B. Davies and E.O. Hiltunen and P. Liu

(Report number 2023-34)

Abstract
This paper shows that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of an imaginary gauge potential, which leads to a skin effect that is manifested by the system's eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate the competition between the two different localisation effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localisation. We show that, as the strength of the disorder increases, more and more eigenmodes become localised in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalised also to tight-binding models in condensed matter theory.

Keywords: Non-Hermitian systems, non-Hermitian skin effect, subwavelength resonators, imaginary gauge potential, Toeplitz matrix, eigenvector condensation, Anderson localisation, stability analysis, disorder-induced phase transition.

@Techreport{ABDHL23_1071,
  author = {H. Ammari and S. Barandun and B. Davies and E.O. Hiltunen and P. Liu},
  title = {Stability of the non-Hermitian skin effect},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-34},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-34.pdf },
  year = {2023}
}

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