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arXiv · 2506.19229

Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles

Kei Matsushima·Takayuki Yamada
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Abstract

This paper is concerned with non-Hermitian degeneracy and exceptional points associated with resonances in an acoustic scattering problem with sound-hard obstacles. The aim is to find non-Hermitian degenerate (defective) resonances using numerical methods. To this end, we characterize resonances of the scattering problem as eigenvalues of a holomorphic integral operator-valued function. This allows us to define defective resonances and associated exceptional points based on the geometric and algebraic multiplicities. Based on the theory on holomorphic Fredholm operator-valued functions, we show fractional-order sensitivity of defective resonances with respect to operator perturbation. This property is particularly important in physics and associated with intriguing phenomena, e.g., enhanced sensing and dissipation. A defective resonance is sought based on the perturbation analysis and Nyström discretization of the boundary integral equation. Numerical evidence of the existence of a defective resonance is provided. The numerical results combined with theoretical analysis provide a new insight into novel concepts in non-Hermitian physics.

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Kei Matsushima, Takayuki Yamada. 2025-06-24. Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles. https://doi.org/10.1098/rspa.2025.0230

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