Spectra and pseudo-spectra of tridiagonal k-Toeplitz matrices and the topological origin of the non-Hermitian skin effect
METADATA ONLY
Loading...
Author / Producer
Date
2024-01
Publication Type
Report
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
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 [H. Ammari et al., arXiv:2307.13551]. We also numerically verify our theory for these systems.
Permanent link
Publication status
published
Editor
Book title
Journal / series
Volume
2024-05
Pages / Article No.
Publisher
Seminar for Applied Mathematics, ETH Zurich
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Tridiagonal k-Toeplitz operator; Block-Toeplitz operator; Tridiagonal k-Laurent operator; Pseudospectra; Coburn's lemma; Non-Hermitian skin effect; Gauge capacitance matrix; Eigenmode condensation
Organisational unit
09504 - Ammari, Habib / Ammari, Habib
Notes
Funding
200307 - Mathematics of dielectric artificial media (SNF)
Related publications and datasets
Is previous version of: