  We show that viscoelastic effects play a crucial role in the damping of
vibrational modes in harmonic amorphous solids. The relaxation of a given plane
wave is described by a memory function of a semi-infinite one-dimensions
mass-spring chain. The initial vibrational energy spreads from the first site
of the chain to infinity. In the beginning of the chain, there is a barrier,
which significantly reduces the decay of vibrational energy below the
Ioffe-Regel frequency. To obtain the parameters of the chain, we present a
numerically stable method, based on the Chebyshev expansion of the local
vibrational density of states.
