  We show that the distinct differences of low-lying THz-frequency dynamics
between type-I clathrates with on-center and off-center guest ions naturally
follow from a theoretical model taking into account essential features of the
dynamics of rattling guest ions. Our model analysis demonstrates the drastic
change from the conventional dynamics shown by on-center systems to the
peculiar dynamics of off-center systems in a unified manner. We claim that
glass-like plateau thermal conductivities observed for off-center systems stem
from the flattening of acoustic phonon dispersion in the regime |k|<|G|/4. The
mechanism is applicable to other systems such as glasses or relaxers.
