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

• URL: http://arxiv.org/abs/2508.05039v1
• Date: Thu, 07 Aug 2025 05:42:51 GMT
• Title: Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies
• Authors: Kaiyuan Wang, Niall Byrnes, Matthew R. Foreman,
• Abstract summary: Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations.<n>We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies.
• Score: 3.092042419611666
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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