Spectral statistics and wave-chaos transition in three-dimensional acoustic cavities

Abstract We numerically study three-dimensional acoustic cavities with progressively increasing geometric complexity and analyze their spectral and spatial statistics. The eigenfrequency spectra and adjacent level-spacing ratios reveal a clear transition from Poisson to Gaussian orthogonal ensemble (GOE) statistics as the cavity structure becomes more irregular. The intermediate regimes are quantitatively characterized using the Berry–Robnik (BR) and Brody distributions, which yield consistent estimates of the chaotic fraction. Furthermore, both the participation ratio and long-range spectral correlations confirm the continuous evolution from integrable to chaotic dynamics. The distributions of normalized wavefunction amplitudes gradually approach the Gaussian prediction, indicating the onset of wave chaos. These results demonstrate that three-dimensional acoustic resonators provide a numerically controllable and experimentally accessible platform for studying the universal transition from Poisson to GOE statistics and for exploring the interplay between geometry and wave chaos.