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

Ioffe-Regel criterion and viscoelastic properties of amorphous solids