Spectral Rigidity in the Large Modal Overlap Regime: Beyond the Ericson-Schroeder Hypothesis

Abstract

Spectral correlations for the total cross section in chaotic scattering or, alternatively, for the resonance density function in chaotic reverberant rooms, are studied within the frame of the random matrix theory. This framework allows us to develop a theory of spectral correlations in the large modal overlap regime which goes beyond the Ericson- Schroeder result of Lorentzian autocorrelation functions. Spectral rigidity is shown to lead to a different autocorrelation function which is universal in the limit of large resonance overlap. Numerical evidence for this signature of spectral rigidity is given within the frame of a 2-dimensional chaotic billiard model of a reverberant room, for which level repulsion and spectral rigidity are known to be well described by the Gaussian Orthogonal Ensemble in the absence of absorption.