Elastic constant inhomogeneity and the broadening of the dynamic structurefactor in one-dimensional disordered systems

The dynamical structure factor of a model disordered system consisting of s pring-disordered harmonic linear chains is studied both analytically and nu merically. The: width of the acoustic excitation peak is observed to grow q uadratically with the exchanged momentum Q; such behavior is shown to be du e to spatial fluctuations of the local wavelength of the collective vibrati onal modes, which in turn is produced by the inhomogeneity of the interpart icle elastic constants. The extent to which this mechanism can explain the Q(2)-dependent broadening recently observed in many glasses both experiment ally and numerically is discussed.