Mathematical foundations of the non-Hermitian skin effect

H Ammari, S Barandun, J Cao, B Davies… - Archive for Rational …, 2024 - Springer
We study the skin effect in a one-dimensional system of finitely many subwavelength
resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we …

Edge modes in subwavelength resonators in one dimension

H Ammari, S Barandun, J Cao, F Feppon - Multiscale Modeling & Simulation, 2023 - SIAM
We present the mathematical theory of one-dimensional infinitely periodic chains of
subwavelength resonators. We analyze both Hermitian and non-Hermitian systems …

Exponentially localized interface eigenmodes in finite chains of resonators

H Ammari, S Barandun, B Davies… - Studies in Applied …, 2024 - Wiley Online Library
This paper studies wave localization in chains of finitely many resonators. There is an
extensive theory predicting the existence of localized modes induced by defects in infinitely …

Spectral convergence in large finite resonator arrays: the essential spectrum and band structure

H Ammari, B Davies, EO Hiltunen - Bulletin of the London …, 2023 - Wiley Online Library
We show that the resonant frequencies of a system of coupled resonators in a truncated
periodic lattice converge to the essential spectrum of the corresponding infinite lattice. We …

The non-Hermitian skin effect with three-dimensional long-range coupling

H Ammari, S Barandun, J Cao, B Davies… - arXiv preprint arXiv …, 2023 - arxiv.org
We study the non-Hermitian skin effect in a three-dimensional system of finitely many
subwavelength resonators with an imaginary gauge potential. We introduce a discrete …

Space-Time Wave Localisation in Systems of Subwavelength Resonators

H Ammari, EO Hiltunen, L Rueff - arXiv preprint arXiv:2409.10100, 2024 - arxiv.org
In this paper we study the dynamics of metamaterials composed of high-contrast
subwavelength resonators and show the existence of localised modes in such a setting. A …

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

H Ammari, S Barandun, A Uhlmann - arXiv preprint arXiv:2410.17597, 2024 - arxiv.org
Truncated Floquet-Bloch transform for computing the spectral properties of large finite systems
of resonators Page 1 Truncated Floquet-Bloch transform for computing the spectral properties of …

Subwavelength Localisation in Disordered Systems

H Ammari, S Barandun, A Uhlmann - arXiv preprint arXiv:2412.13954, 2024 - arxiv.org
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 …

Design of defected non-hermitian chains of resonator dimers for spatial and spatio-temporal localizations

H Ammari, EO Hiltunen, T Kosche - SIAM Journal on Applied Mathematics, 2023 - SIAM
The aim of this article is to advance the field of metamaterials by proposing formulas for the
design of high-contrast metamaterials with prescribed subwavelength defect mode …

Mathematical Foundation for Symmetry Breaking in Subwavelength Physics

J Cao - 2024 - research-collection.ethz.ch
The control and manipulation of wave-matter interactions at subwavelength scales
constitutes an important realm within wave physics. Topological insulators with …