声子蒙特卡罗：产生热输运模拟的随机变量
Phonon Monte Carlo: Generating Random Variates for Thermal Transport Simulation
摘要：
声子蒙特卡罗（PMC）是一种求解声子玻尔兹曼输运方程的通用随机技术。它特别适合于分析具有真实空间粗糙度或太大而无法直接使用原子技术模拟的结构中的热传输。PMC取决于\textit{random variates}的生成和使用--对应于物理观测值的随机变量的特定值--以准确有效地捕获适当的分布函数的方式。我们提出的反演和拒绝技术的相对优点，用于产生随机变量的几个例子相关的热输运：绘制声子的热分布和充分或各向同性的色散，随机传出的动量扩散边界散射后，实施接触（边界和内部），并保存在模拟中的能量。我们还确定了声子生成和散射中的共同主题，这有助于在模拟中重用代码（生成热声子属性与内部接触;漫反射表面散射与边界接触）。我们希望这些例子将告知读者随机变量生成的机制，以及如何为手头的任何问题选择一个好的方法，并帮助PMC更广泛地用于热输运模拟。
英文摘要：
Phonon Monte Carlo (PMC) is a versatile stochasic technique for solving the Boltzmann transport equation for phonons. It is particularly well suited for analyzing thermal transport in structures that have real-space roughness or are too large to simulate directly using atomistic techniques. PMC hinges on the generation and use of \textit{random variates} -- specific values of the random variables that correspond to physical observables -- in a way that accurately and efficiently captures the appropriate distribution functions. We present the relative merits of the inversion and rejection techniques for generating random variates on several examples relevant in thermal transport: drawing phonons from a thermal distribution and with full or isotropic dispersion, randomizing outgoing momentum upon diffuse boundary scattering, implementing contacts (boundary and internal), and conserving energy in the simulation. We also identify common themes in phonon generation and scattering that are helpful for reusing code in the simulation (generating thermal-phonon attributes vs internal contacts; diffuse surface scattering vs boundary contacts). We hope these examples will inform the reader about the mechanics of random-variate generation and how to choose a good approach for whatever problem is at hand, and aid in the more widespread use of PMC for thermal transport simulation.
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