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Mathematical Origin of the Non-Hermitian Skin Effect

Authors: Habib Ammari, Silvio Barandun, Yannick De Bruijn, Ping Liu, Clemens Thalhammer

Venue: Journal of Physics A: Mathematical and Theoretical (2025)

Status: Published

Published:

DOI
non-hermitian physics spectral theory topological physics

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 expo- nential 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. We also numerically verify our theory for these polymer systems.

Bibtex

@article{ammari2025spectra,
  title={Spectra and pseudo-spectra of tridiagonal k-Toeplitz matrices and the topological origin of the non-Hermitian skin effect},
  author={Ammari, Habib and Barandun, Silvio and De Bruijn, Yannick and Liu, Ping and Thalhammer, Clemens},
  journal={Journal of Physics A: Mathematical and Theoretical},
  volume={58},
  number={20},
  pages={205201},
  year={2025},
  publisher={IOP Publishing}
}