Excited resonance widths for Helmholtz resonators with straight neck

TL;DR

This paper extends the understanding of resonance widths in Helmholtz resonators by providing exponential lower bounds for excited states, under specific geometric assumptions, generalizing previous results for the ground state.

Contribution

It generalizes the exponential lower bound on resonance widths from ground to excited eigenstates in Helmholtz resonators with straight necks, under certain conditions.

Findings

Established exponential lower bounds for excited resonance widths.

Generalized previous results from ground to excited states.

Provided conditions under which the bounds hold.

Abstract

We consider resonances associated with excited eigenvalues of the cavity of a general Helmholtz resonator with straight neck. Under the assumption that the neck stays away from the nodal set of the corresponding eigenstate, we generalise the optimal exponential lower bound on the width of the resonance, that we have obtained in a previous paper for the ground resonance only.