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

2025/08/07 by Wang, Kaiyuan, Byrnes, Niall, Foreman, Matthew R.
#FOS: Physical sciences #Mathematical Physics (math-ph) #Optics (physics.optics) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.05039

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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