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

TL;DR

This paper investigates non-Hermitian degeneracies called exceptional points in acoustic scattering with sound-hard obstacles, using numerical methods to identify defective resonances and analyze their sensitivity, contributing to non-Hermitian physics understanding.

Contribution

It introduces a numerical approach to find defective resonances and exceptional points in acoustic scattering, linking them to non-Hermitian physics phenomena.

Findings

Existence of defective resonances demonstrated numerically.

Fractional-order sensitivity of resonances to perturbations shown.

New insights into non-Hermitian physics provided.

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 Nystr\"om 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.