Elastic Constant Inhomogeneity and the Broadening of the Dynamic Structure Factor in One-Dimensional Disordered Systems

The dynamical structure factor of a model disordered system consisting of spring-disordered harmonic linear chains is studied both analytically and numerically. The width of the acoustic excitation peak is observed to grow quadratically with the exchanged momentum Q; such behavior is shown to be due to spatial fluctuations of the local wavelength of the collective vibrational modes, which in turn is produced by the inhomogeneity of the interparticle elastic constants. The extent to which this mechanism can explain the Q2-dependent broadening recently observed in many glasses both experimentally and numerically is discussed.