J. Phys. I France 5 (1995) 1003-1010
Spectral Rigidity in the Large Modal Overlap Regime: Beyond the Ericson-Schroeder HypothesisOlivier Legrand, Fabrice Mortessagne and Didier Sornette
Laboratoire de Physique de la Matière Condensée (CNRS URA 190), Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France and X-RS, Parc-Club - 28, rue Jean Rostand, 91893 Orsay Cedex, France
(Received 27 March 1995, accepted 4 May 1995)
Spectral correlations for the total cross section in choatic 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.
© Les Editions de Physique 1995