用于流体动力学第二声建模的多维玻尔兹曼输运方程解析格林函数
Analytical Green's Function of Multidimensional Boltzmann Transport Equation for Modeling Hydrodynamic Second Sound
AI总结：
针对多维声子流体动力学输运建模难题，本文提出基于第一性原理声子性质与Callaway近似的BTE解析格林函数，可高效再现弹道、流体动力学和扩散区转变并准确预测温度振荡。
摘要：
当声子-声子相互作用以动量守恒为主时，热脉冲可产生流体动力学第二声，此时温度场的传播呈现波动性而非扩散性。尽管玻尔兹曼输运方程（BTE）已被广泛用于研究纳米尺度的声子动力学和热输运，但对流体动力学输运区进行建模仍然具有挑战性。广泛使用的弛豫时间近似（RTA）将所有声子相互作用都视为阻力性相互作用，而未考虑动量守恒，因此无法描述声子流体动力学。然而，通过求逆完整散射矩阵来严格求解BTE，计算代价极高，而且迄今仅被用于建模一维温度变化。在此，我们提出一种解析格林函数形式体系，利用第一性原理计算得到的声子性质来求解多维BTE。该形式体系采用Callaway散射近似，对动量守恒和动量破坏散射事件分别使用独立的弛豫时间。该格林函数可在很宽的温度、空间和时间尺度范围内捕捉声子动力学，并成功再现从弹道、流体动力学到扩散输运区的转变。我们的方法避免了对大型散射矩阵进行高计算代价的求逆，并在预测不同热激发几何结构的超快泵浦-探测表征中的温度振荡时表现出良好精度。
英文摘要：
Hydrodynamic second sound can be generated by heat pulses when the phonon-phonon interaction is dominantly momentum conserving, and the propagation of the temperature field becomes wavelike rather than diffusive. While the Boltzmann transport equation (BTE) has been widely applied to study phonon dynamics and thermal transport at the nanoscale, modeling the hydrodynamic transport regime remains challenging. The widely used relaxation time approximation (RTA) treats all phonon interactions as resistive without considering momentum conservation, resulting in the absence of phonon hydrodynamics. Rigorously solving BTE by inverting the full scattering matrix, however, is extremely computationally demanding and has been only applied to model one-dimensional temperature variations. Here, we present an analytical Green's function formalism for solving multidimensional Boltzmann transport equation (BTE) using phonon properties from first-principles calculations. This formalism involves Callaway's scattering approximation with separate relaxation times for momentum-conserving and momentum-destroying scattering events. The Green's function captures phonon dynamics in a wide range of temperature, spatial, and temporal scales, and successfully reproduces the transition from ballistic, hydrodynamic, to diffusive transport regimes. Our method avoids the computationally demanding inversion of large scattering matrices and shows good accuracies in predicting the temperature oscillation in ultrafast pump-probe characterizations with different geometries of thermal excitation.
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