Yannick De Bruijn

• Bruijn, Yannick De & Hiltunen, Erik Orvehed (2026). Mathematical Foundation for the Generalised Brillouin zone of m-banded Toeplitz operators. arXiv. doi: 10.48550/ARXIV.2602.09734. Full text in Research Archive
• Bruijn, Yannick De & Hiltunen, Erik Orvehed (2026). Complex Brillouin zone for localised modes in Hermitian and non-Hermitian problems. Communications in nonlinear science & numerical simulation. ISSN 1007-5704. 161, p. 110014–110014. doi: 10.1016/j.cnsns.2026.110014. Full text in Research Archive
• Bruijn, Yannick De; Davies, Bryn; Dupuy, Sacha & Hiltunen, Erik Orvehed (2025). Spectra and pseudospectra of non-Hermitian Toeplitz operators: Eigenvector decay transitions in banded and dense matrices. arXiv. doi: 10.48550/ARXIV.2512.03757. Full text in Research Archive
• Bruijn, Yannick De & Hiltunen, Erik Orvehed (2025). Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects. arXiv. doi: 10.48550/ARXIV.2505.23610. Full text in Research Archive
• Ammari, Habib; Barandun, Silvio; Bruijn, Yannick De; Liu, Ping & Thalhammer, Clemens (2025). Spectra and pseudo-spectra of tridiagonal k-Toeplitz matrices and the topological origin of the non-Hermitian skin effect. Journal of Physics A: Mathematical and Theoretical. ISSN 1751-8113. 58(20), p. 205201–205201. doi: 10.1088/1751-8121/add5ab. Full text in Research Archive Show summary

  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. We also numerically verify our theory for these polymer systems.

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