Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects
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2025-06
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Report
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Abstract
Using the Bloch-Floquet theory, we propose an innovative technique to obtain the eigenvectors of tridiagonal k-Toeplitz operators. This method offers a more extensive and quantitative basis for describing localised eigenvectors beyond the non-trivial winding zone, yielding sharp decay bounds. The validity of our results is confirmed numerically in one-dimensional resonator chains, showcasing non-Hermitian skin localisation, bulk localisation, and tunnelling effects. We conclude the paper by analysing non-Hermitian tight binding Hamiltonians, illustrating the broad applicability of the complex band structure.
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published
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2025-17
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Tridiagonal k-Toeplitz operator; Block-Toeplitz operator; Subwavelength resonances; Evanescent modes; Band gap; Non-Hermitian skin effect; Eigenmode condensation; Non-Hermitian defected metamaterials; Topological phase transition; Non-Hermitian Hamiltonian; Pseudospectra; Bloch theory; Complex Brillouin zone
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09504 - Ammari, Habib / Ammari, Habib