AI 中文总结
本综述梳理了从量子声子戴森方程到介观声子流体动力学的热输运理论框架，推导了相关方程的极限形式，关联了微观物理与可观测非扩散热输运现象，为该领域研究提供路线图。
AI 中文摘要
介电非磁性晶体中的热输运由量子化晶格振动介导，当这些晶格振动受温度梯度驱动偏离平衡时，会发生漂移与相互作用。该现象可通过多个理论层面描述，范围从全量子描述到半经典及介观连续介质方法。本综述严格探讨连接这些层面的理论步骤与近似，弥合量子声子戴森方程、Kadanoff-Baym方程与半经典玻尔兹曼输运形式，并讨论粗粒化过程，该过程可生成适用于器件中非扩散流体热输运的介观粘性热方程。我们展示了Guyer-Krumhansl方程与双相滞后方程如何分别作为粘性热方程的特殊线性各向同性带极限与无粘性极限；最重要的是，我们证明这些方程不仅能预测泊肃叶流与第二声，还能预测更奇特的效应，如负热阻、稳态热回流及涡旋。我们强调将这些框架与第一性原理模拟结合，可将微观声子物理与可观测的非扩散热输运现象关联起来，并指导其探测、放大与控制。我们将粘性热方程重新表述为亥姆霍兹方程与双调和方程的形式，通过解析求解，以此讨论声子流体与其他流体动力学系统（如经典流体与电子流体）宏观行为的异同，聚焦于可压缩性、涡度及其对声子流体动力学的影响。最后，我们提出将描述声子流体动力学的工具推广到其他准粒子的路线图，为固体中集体量子输运现象的未来进展提供动力。
英文摘要
Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.
Comments165 pages, 34 figures, 3 tables
Journal refDi Lucente, E., Simoncelli, M., & Marzari, N. (2026). Thermal transport in crystals: from the quantum Dyson equation to mesoscopic phonon hydrodynamics. Advances in Physics, 1-140
DOI：10.1080/00018732.2026.2685376
