In heat conduction through a homogenous nanomaterial, various phonons may exhibit diverse temperatures even at the same location at a steady state, known as the local phonon nonequilibrium phenomenon. Different phonons are often considered to behave independently, and the phonons with longer mean free paths (MFPs) have smaller temperature gradients. That is, the temperature gradient exhibits the following order: ballistic phonons < semiballistic phonons ≈ lattice (average) temperature gradient < diffusive phonons, where ballistic phonons have MFPs much larger than the characteristic length, semiballistic phonons have MFPs like the characteristic length, and diffusive phonons have MFPs much smaller than the characteristic length. However, in this paper, we reveal that the effect of phonon-phonon coupling leads nonequilibrium phonon temperature gradients to the following trend: diffusive phonon temperature gradients will decrease to the lattice temperature, and temperature gradients of some semiballistic phonons even surpass that of diffusive phonons. The diffusive phonon temperature is merged onto the lattice temperature since they have large scattering rates and can be equilibrated quickly to the lattice temperature after traveling for a short distance away from the boundaries into the nanomaterial. The semiballistic phonons have large scattering rates but not large enough to bring them down to the lattice temperature. To obtain a further understanding of the nonequilibrium phonon temperatures, we have also derived a simple analytical model which can accurately predict the temperature profiles of all individual phonons given their MFPs. Using this model, we find that, near the boundary, phonon temperatures decay with position exponentially (instead of linearly), with a rate inversely proportional to their MFPs. Our findings offer insight for the understanding and prediction of phonon nonequilibrium temperatures within nanodevices.

中文翻译：

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由有限尺寸引起的非平衡声子传输：声子-声子耦合的影响

在通过同质纳米材料进行热传导时，即使在稳定状态下的同一位置，各种声子也可能表现出不同的温度，这被称为局部声子非平衡现象。不同的声子通常被认为是独立行为的，平均自由程（MFP）较长的声子具有较小的温度梯度。也就是说，温度梯度表现出以下顺序：弹道声子 < 半弹道声子 ≈ 晶格（平均）温度梯度 < 扩散声子，其中弹道声子的 MFP 远大于特征长度，半弹道声子的 MFP 与特征长度一样，扩散声子的 MFP 远小于特征长度。然而，在这篇论文中，我们揭示了声子-声子耦合的影响导致非平衡声子温度梯度呈现以下趋势：扩散声子温度梯度将降低到晶格温度，并且一些半弹道声子的温度梯度甚至超过扩散声子的温度梯度。扩散声子温度合并到晶格温度上，因为它们具有大的散射率，并且在离开边界进入纳米材料的一小段距离后可以快速平衡到晶格温度。半弹道声子具有较大的散射率，但不足以将它们降低到晶格温度。为了进一步了解非平衡声子温度，我们还推导出了一个简单的分析模型，该模型可以准确预测给定 MFP 的所有单个声子的温度分布。使用该模型，我们发现，在边界附近，声子温度随位置呈指数（而不是线性）衰减，其速率与其 MFP 成反比。我们的发现为理解和预测纳米器件内的声子非平衡温度提供了见解。