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 elastic wave is described by a memory function of a semi-infinite one-dimensional 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.

中文翻译：

---

无定形固体的Ioffe-Regel准则和粘弹性

我们表明，粘弹性效应在谐波无定形固体中振动模式的阻尼中起着至关重要的作用。给定平面弹性波的松弛是通过半无限一维质量弹簧链的记忆函数来描述的。初始振动能量从链的第一个位置传播到无穷大。在链的开头，有一个屏障，可显着降低振动能量在艾菲尔-雷格尔频率以下的衰减。为了获得链的参数，我们基于状态的局部振动密度的切比雪夫展开，提出了一种数值稳定的方法。