Level repulsion and spectral rigidity in reverberant microwave cavities

Abstract

It is now widely acknowledged that spectral fluctuations of waves in complex systems are well described by random matrix theory. As a model system for complex or disordered reverberant cavities, a two-dimensional reverberant microwave cavity is investigated in a high-frequency regime where resonances are still below the large modal overlap regime. Modifying the cavity through the inclusion of scatterers makes the dynamics of rays chaotic or diffusive, thus rendering its spectral response strongly correlated over short and long frequency range. This can be illustrated by the distribution of frequency spacings between neighboring resonances which clearly exhibits the so-called level repulsion. Longer range correlations are demonstrated by considering an averaged time response of the cavity for times shorter than the inverse modal density. By scaling down the hyperfrequency range to audio frequency range and proper sampling, an auditive perception of the differences between the spectral responses of a regular (pure rectangular cavity) and a complex reverberant cavity is demonstrated.