He Dahai, Buyukdagli Sahin, Hu Bambi
Department of Physics, Centre for Nonlinear Studies, and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061103. doi: 10.1103/PhysRevE.78.061103. Epub 2008 Dec 2.
We compare two effective phonon theories, which have both been applied recently to study heat conduction in anharmonic lattices. In particular, we study the temperature dependence of the thermal conductivity of the Fermi-Pasta-Ulam beta model via the Debye formula, showing the equivalence of both approaches. The temperature for the minimum of the thermal conductivity and the corresponding scaling behavior are analytically calculated, which agree well with the result obtained from nonequilibrium simulations. We also give quantum corrections for the thermal conductivity from quantum self-consistent phonon theory. The vanishing behavior at the low temperature regime and the existence of an umklapp peak are qualitatively consistent with experimental studies.
我们比较了两种有效的声子理论，这两种理论最近都被用于研究非谐晶格中的热传导。特别地，我们通过德拜公式研究了费米-帕斯塔-乌拉姆β模型热导率的温度依赖性，展示了两种方法的等效性。通过解析计算得到了热导率最小值对应的温度以及相应的标度行为，这与非平衡模拟得到的结果吻合得很好。我们还给出了量子自洽声子理论对热导率的量子修正。低温区的消失行为以及倒格矢散射峰的存在与实验研究在定性上是一致的。
