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arXiv · 2307.13551

Perturbed Block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators

Habib Ammari·Silvio Barandun·Ping Liu
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Abstract

The aim of this paper is fourfold: (i) to obtain explicit formulas for the eigenpairs of perturbed tridiagonal block Toeplitz matrices; (ii) to make use of such formulas in order to provide a mathematical justification of the non-Hermitian skin effect in dimer systems by proving the condensation of the system's bulk eigenmodes at one of the edges of the system; (iii) to show the topological origin of the non-Hermitian skin effect for dimer systems and (iv) to prove localisation of the interface modes between two dimer structures with non-Hermitian gauge potentials of opposite signs based on new estimates of the decay of the entries of the eigenvectors of block matrices with mirrored blocks.

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Habib Ammari, Silvio Barandun, Ping Liu. 2023-07-25. Perturbed Block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators. https://arxiv.org/abs/2307.13551

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