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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2509.22417 |
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| _version_ | 1866911178589995008 |
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| author | Ammari, Habib Thalhammer, Clemens Uhlmann, Alexander |
| author_facet | Ammari, Habib Thalhammer, Clemens Uhlmann, Alexander |
| contents | We aim to characterise the spectral distributions of bi-infinite, semi-infinite, and finite aperiodic one-dimensional arrays of subwavelength resonators, constructed by sampling from a finite library of building blocks. By adopting the modern formalism of uniform hyperbolicity, we are able to strengthen and rigorously prove a Saxon-Hutner-type result, fully characterising the spectral gaps of the composite bi-infinite aperiodic system in terms of its constituent blocks. Crucial to this approach is a change of basis from transfer matrices to propagation matrices, allowing for a block-level characterisation. This approach also enables an explicit characterisation of edge-induced eigenmodes in the semi-infinite setting. Finally, we leverage finite section methods for Jacobi operators to extend our results to finite systems - providing strict bounds for their spectra in terms of their constituent blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators Ammari, Habib Thalhammer, Clemens Uhlmann, Alexander Mathematical Physics Disordered Systems and Neural Networks Dynamical Systems 35J05, 35P20, 37D20, 37A30, 47B36 We aim to characterise the spectral distributions of bi-infinite, semi-infinite, and finite aperiodic one-dimensional arrays of subwavelength resonators, constructed by sampling from a finite library of building blocks. By adopting the modern formalism of uniform hyperbolicity, we are able to strengthen and rigorously prove a Saxon-Hutner-type result, fully characterising the spectral gaps of the composite bi-infinite aperiodic system in terms of its constituent blocks. Crucial to this approach is a change of basis from transfer matrices to propagation matrices, allowing for a block-level characterisation. This approach also enables an explicit characterisation of edge-induced eigenmodes in the semi-infinite setting. Finally, we leverage finite section methods for Jacobi operators to extend our results to finite systems - providing strict bounds for their spectra in terms of their constituent blocks. |
| title | Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators |
| topic | Mathematical Physics Disordered Systems and Neural Networks Dynamical Systems 35J05, 35P20, 37D20, 37A30, 47B36 |
| url | https://arxiv.org/abs/2509.22417 |