We present theoretical investigation on the high-frequency collective
dynamics in liquids and glasses at microscopic length scales and terahertz
frequency region based on the mode-coupling theory for ideal liquid-glass
transition. We focus on recently investigated issues from
inelastic-X-ray-scattering and computer-simulation studies for dynamic
structure factors and longitudinal and transversal current spectra: the
anomalous dispersion of the high-frequency sound velocity and the nature of the
low-frequency excitation called the boson peak. It will be discussed how the
sound mode interferes with other low-lying modes present in the system.
Thereby, we provide a systematic explanation of the anomalous sound-velocity
dispersion in systems -- ranging from high temperature liquid down to deep
inside the glass state -- in terms of the contributions from the
structural-relaxation processes and from vibrational excitations called the
anomalous-oscillation peak (AOP). A possibility of observing negative
dispersion -- the {\em decrease} of the sound velocity upon increase of the
wave number -- is argued when the sound-velocity dispersion is dominated by the
contribution from the vibrational dynamics. We also show that the low-frequency
excitation, observable in both of the glass-state longitudinal and transversal
current spectra at the same resonance frequency, is the manifestation of the
AOP. As a consequence of the presence of the AOP in the transversal current
spectra, it is predicted that the transversal sound velocity also exhibits the
anomalous dispersion. These results of the theory are demonstrated for a model
of the Lennard-Jones system.Comment: 25 pages, 22 figure