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arXiv 2008.07596cond-mat.mes-hall
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非局域热输运中的时空相关热导率

Space-time dependent thermal conductivity in nonlocal thermal transport

Chengyun Hua, Lucas Lindsay

摘要:

非局域热输运一般由Peierls-Boltzmann输运方程(PBE)描述。然而,解决一般的时空相关问题的PBE仍然是一个具有挑战性的任务,由于高维的积分微分方程。在这项工作中,我们提出了一个直接的解决方案的时空依赖PBE与线性碰撞矩阵使用本征分解方法。我们发现,存在一个广义的傅立叶型关系,连接热通量的本地温度,和本构关系定义的热导率,取决于时间和空间。结合这种方法与声子性质的从头计算,我们证明了时空相关的热导率引起的瞬态光栅几何形状在高热导率材料的温度振荡响应。本解决方案的方法使我们能够扩展我们的热传导的计算能力,时空相关的非扩散运输制度。这种能力不仅可以更准确地解释观察非局部热传输的热测量,而且还可以增强我们对高热导率材料中非局部热传输的物理理解,这些材料是纳米级热管理应用的有希望的候选者。

英文摘要:

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. This capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

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