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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.23610 |
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| _version_ | 1866918038234726400 |
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| author | De Bruijn, Yannick Hiltunen, Erik Orvehed |
| author_facet | De Bruijn, Yannick Hiltunen, Erik Orvehed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects De Bruijn, Yannick Hiltunen, Erik Orvehed Analysis of PDEs 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. |
| title | Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.23610 |