High-frequency asymptotics and random matrix theory in reverberant rooms

Abstract

It is now recognized that in the low-frequency range below Schroeder’s cutoff a modal approach of the spectral fluctuations in a reverberant room is appropriate. Indeed, in his experimental study of the modal frequencies in a reverberation room, Davy [J. L. Davy, Proc. Inter-Noise, 159–164 (1990)] confirmed that the level repulsion is in good accord with the predictions of the Wigner–Dyson’s random matrix Theory (RMT). In Quantum Chaology many works have tried to understand the link between the observed spectral statistics of wave cavities which are known to be chaotic in the limit of rays and the statistics of eigenvalues of random matrices. Here this matter is addressed in the context of room acoustics by considering an asymptotic representation of the response in chaotic rooms in terms of periodic rays. Various results are established concerning universal aspects of the spectral fluctuations recovering predictions of RMT both in the moderate and large modal overlap regimes [O. Legrand and F. Mortessagne, Acustica–acta acustica 82 (Suppl. 1), S150 (1996)]. The results are illustrated in a two-dimensional chaotic enclosure using a semiclassical Green’s function formalism [F. Mortessagne and O. Legrand, Acustica–acta acustica 82 (Suppl. 1), S152 (1996)].