Spectra and pseudo-spectra of tridiagonal k-Toeplitz matrices and the topological origin of the non-Hermitian skin effect

2024/01/23 by Habib Ammari, Ammari, Habib, S Barandun +7 · 3 citations
Physics and Astronomy · #15A18 #15B05 #81Q12 #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Optics (physics.optics) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.12626

openalex publication_date 2024/01/23 · openalex created_date 2024/01/25 · openalex updated_date 2026/08/01

Abstract

We establish new results on the spectra and pseudo-spectra of tridiagonal k-Toeplitz operators and matrices. In particular, we prove the connection between the winding number of the eigenvalues of the symbol function and the exponential decay of the associated eigenvectors (or pseudo-eigenvectors). Our results elucidate the topological origin of the non-Hermitian skin effect in general one-dimensional polymer systems of subwavelength resonators with imaginary gauge potentials, proving the observation and conjecture in arXiv:2307.13551. We also numerically verify our theory for these systems.

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