Vibrations in glasses and Euclidean random matrix theory

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peal: and secondary peak), Euclidean random matrix theory provides a single and fairly simple theoretical framework for their explanation.