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arXiv · 2508.05039

Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies

Kaiyuan Wang·Niall Byrnes·Matthew R. Foreman
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Abstract

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.

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Kaiyuan Wang, Niall Byrnes, Matthew R. Foreman. 2025-12-30. Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies. https://doi.org/10.1364/ol.575813

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