Lattice heat-current time correlation functions for insulators and semiconductors obtained using molecular dynamics (MD) simulations exhibit features of both pure exponential decay and oscillatory-exponential decay. For some materials the oscillatory terms contribute significantly to the lattice heat conductivity calculated from the correlation functions. However, the origin of the oscillatory terms is not well understood, and their contribution to the heat conductivity is accounted for by fitting them to empirical functions. Here, a translationally invariant expression for the heat current in terms of creation and annihilation operators is derived. By using this full phonon-picture definition of the heat current and applying the relaxation-time approximation we explain, at least in part, the origin of the oscillatory terms in the lattice heat-current correlation function. We discuss the relationship between the crystal Hamiltonian and the magnitude of the oscillatory terms. A solvable one-dimensional model is used to illustrate the potential importance of terms that are omitted in the commonly used phonon-picture expression for the heat current. While the derivations are fully quantum mechanical, classical-limit expressions are provided that enable direct contact with classical quantities obtainable from MD.

中文翻译：

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晶格热-电流时间相关函数中振荡项的理论分析及其对热导率的贡献

使用分子动力学（MD）模拟获得的绝缘体和半导体的晶格热-电流时间相关函数显示出纯指数衰减和振荡指数衰减的特征。对于某些材料，振荡项对根据相关函数计算出的晶格热导率有很大贡献。但是，振荡项的起源还不太清楚，并且它们对热导率的贡献是通过将它们拟合为经验函数来解决的。在此，从生成和current灭算符的角度推导了热流的平移不变表达式。通过使用热电流的完整声子图定义并应用弛豫时间近似，我们至少部分地解释了：晶格热电流相关函数中振荡项的起源。我们讨论了晶体哈密顿量和振动项的大小之间的关系。可解决的一维模型用于说明在热电流的常用声子图像表达式中省略的术语的潜在重要性。虽然推导是完全量子力学的，但提供了古典极限表达式，使它们能够直接与可从MD获得的古典量接触。