While it is well known that the vibrational modes are fully occupied and the quantum effect can be ignored only if the temperature is high enough, e.g., well above the Debye temperature of the systems, all vibrational modes are assumed to be fully occupied at any temperatures in classical molecular dynamics. Therefore, the thermal conductivity of crystals predicted by classical molecular dynamics at low temperatures, e.g., much lower than the corresponding Debye temperature, is unphysical. Even by applying the quantum corrections on the classical thermal conductivity of crystals, the results are still unreasonable since both the occupation and intrinsic scattering process of the vibrations are determined by the temperatures. However, the scattering picture in amorphous silicon is quite different from that in its corresponding crystal counterpart. How the quantum effect will affect the thermal transport in amorphous silicon is still unclear. Here, by systematically investigating thermal transport of amorphous silicon using equilibrium molecular dynamics, the structure factor method and the Allen–Feldman theory, we directly observe that all the vibrational modes are fully occupied at any temperatures and the quantum effect on the scattering process can be ignored. By assuming all the vibrational modes are fully occupied, the thermal conductivity calculated using the structure factor method and the Allen–Feldman theory agrees quite well with the results computed using Green–Kubo equilibrium molecular dynamics. By correcting the excitation state of the vibrations in amorphous silicon, the thermal conductivity calculated by the structure factor method and the Allen–Feldman theory can fully capture the experimentally measured temperature dependence. Our study proves that the quantum effect on the scattering process caused by the distribution functions for the amorphous materials in molecular dynamics simulations, i.e., Boltzmann distributions in molecular dynamics simulations vs Bose–Einstein distributions for the bosons, can be ignored, while the quantum effect on the excitation states of the vibrations are important and must be considered.

中文翻译：

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评估非晶硅经典热导率的量子效应

众所周知，振动模式被完全占据并且只有在温度足够高时才可以忽略量子效应，例如，远高于系统的德拜温度，但假设所有振动模式在任何温度下都被完全占据在经典分子动力学中。因此，通过经典分子动力学在低温下（例如远低于相应的德拜温度）预测的晶体的热导率是非物理的。即使对晶体的经典热导率应用量子校正，结果仍然不合理，因为振动的占据和本征散射过程都由温度决定。然而，非晶硅中的散射图像与其对应的晶体对应物的散射图像完全不同。量子效应将如何影响非晶硅中的热传输仍不清楚。在这里，通过使用平衡分子动力学、结构因子方法和 Allen-Feldman 理论系统地研究非晶硅的热传输，我们直接观察到所有振动模式在任何温度下都被完全占据，并且散射过程的量子效应可以是忽略。假设所有振动模式都被完全占据，使用结构因子方法和 Allen-Feldman 理论计算的热导率与使用 Green-Kubo 平衡分子动力学计算的结果非常吻合。通过校正非晶硅中振动的激发态，通过结构因子法和 Allen-Feldman 理论计算的热导率可以完全捕捉实验测量的温度依赖性。我们的研究证明，分子动力学模拟中非晶材料的分布函数对散射过程的量子效应，即分子动力学模拟中的玻尔兹曼分布与玻色子的玻色-爱因斯坦分布，可以忽略不计，而量子效应振动的激发状态很重要，必须加以考虑。