Evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass tran sitions are used for a discussion of the evolution of the density-fluctuati on spectra of glass-forming systems for frequencies within the dynamical wi ndow between the band of high-frequency motion and the band of low-frequenc y-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wavelength and the arrested g lass structure causes an anomalous-oscillation peak, which exhibits the pro perties of the so-called boson peak. It produces an elastic modulus which g overns the hybridization of density fluctuations of mesoscopic wavelength w ith the boson-peak oscillations. This leads to the existence of high-freque ncy sound with properties as found by x-ray-scattering spectroscopy of glas ses and glassy liquids. The results of the theory are demonstrated for a mo del of the hard-sphere system. It is also derived that certain schematic MC T models, whose spectra for the stiff-glass states can be expressed by elem entary formulas, provide reasonable approximations for the solutions of the general MCT equations. PACS number(s): 64.70.Pf, 63.50.+x, 61.20.Lc.