An atomic-scale theory of the viscoelastic response of metallic glasses is derived from first principles, using a Zwanzig-Caldeira-Leggett system-bath Hamiltonian as a starting point within the framework of nonaffine linear response to mechanical deformation. This approach provides a generalized Langevin equation (GLE) as the average equation of motion for an atom or ion in the material, from which non-Markovian nonaffine viscoelastic moduli are extracted. These can be evaluated using the vibrational density of states (DOS) as input, where the boson peak plays a prominent role in the mechanics. To compare with experimental data for binary ZrCu alloys, a numerical DOS was obtained from simulations of this system, which also take electronic degrees of freedom into account via the embedded-atom method for the interatomic potential. It is shown that the viscoelastic $\alpha$-relaxation, including the $\alpha$-wing asymmetry in the loss modulus, can be very well described by the theory if the memory kernel (the non-Markovian friction) in the GLE is taken to be a stretched-exponential decaying function of time. This finding directly implies strong memory effects in the atomic-scale dynamics and suggests that the $\alpha$-relaxation time is related to the characteristic time scale over which atoms retain memory of their previous collision history. This memory time grows dramatically below the glass transition.

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金属玻璃中粘弹性响应和记忆效应的原子理论

金属玻璃的粘弹性响应的原子尺度理论是从第一原理推导的，使用Zwanzig-Caldeira-Leggett系统-浴哈密顿量作为对机械变形的非仿射线性响应框架的起点。这种方法提供了广义的Langevin方程（GLE），作为材料中原子或离子的平均运动方程，从中提取了非马尔可夫非仿射粘弹性模量。可以使用状态振动密度（DOS）作为输入来评估这些值，其中玻色子峰在力学中起着重要作用。为了与二元ZrCu合金的实验数据进行比较，从该系统的仿真中获得了一个数值DOS，该值也通过嵌入原子方法对原子间电势考虑了电子自由度。$\alpha$-放松，包括 $\alpha$如果将GLE中的记忆核（非马尔科夫摩擦）视为时间的拉伸指数衰减函数，则损耗模量中的双翼不对称性可以用该理论很好地描述。这一发现直接暗示了原子尺度动力学中的强大记忆效应，并表明$\alpha$弛豫时间与原子保留其先前碰撞历史记忆的特征时间标度有关。在玻璃转换以下，此存储时间会急剧增加。