Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917176287428608 |
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| author | Wang, Kaiyuan Byrnes, Niall Foreman, Matthew R. |
| author_facet | Wang, Kaiyuan Byrnes, Niall Foreman, Matthew R. |
| contents | Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations, enabling powerful control and engineering of wave phenomena. We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies using generalized Wigner-Smith operators. We validate our theory using both analytic Hamiltonian models and numerical electromagnetic simulations, demonstrating excellent agreement across a range of cases. Our approach accurately predicts degenerate resonance splitting using only scattering data, offering a powerful framework for precision tuning, inverse design, and practical exploitation of non-Hermitian phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies Wang, Kaiyuan Byrnes, Niall Foreman, Matthew R. Optics Mathematical Physics Quantum Physics Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations, enabling powerful control and engineering of wave phenomena. We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies using generalized Wigner-Smith operators. We validate our theory using both analytic Hamiltonian models and numerical electromagnetic simulations, demonstrating excellent agreement across a range of cases. Our approach accurately predicts degenerate resonance splitting using only scattering data, offering a powerful framework for precision tuning, inverse design, and practical exploitation of non-Hermitian phenomena. |
| title | Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies |
| topic | Optics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2508.05039 |