Hu Bambi, Yang Lei
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.
Chaos. 2005 Mar;15(1):15119. doi: 10.1063/1.1862552.
Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name almost 200 years ago, a first-principle derivation of this simple law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are far from clear. In this paper we will review recent works on heat conduction in a simple nonintegrable model called the Frenkel-Kontorova model. The thermal conductivity of this model has been found to be finite. We will study the dependence of the thermal conductivity on the temperature and other parameters of the model such as the strength and the periodicity of the external potential. We will also discuss other related problems such as phase transitions and finite-size effects. The study of heat conduction is not only of theoretical interest but also of practical interest. We will show various recent designs of thermal rectifiers and thermal diodes by coupling nonlinear chains together. The study of heat conduction in low dimensions is also important to the understanding of the thermal properties of carbon nanotubes.
热传导是一个古老但重要的问题。自近200年前傅里叶提出以他的名字命名的定律以来，从统计力学对这个简单定律进行第一性原理推导仍然缺失。更糟糕的是，该定律在低维情况下的有效性以及其有效性的充要条件还远不清楚。在本文中，我们将回顾关于一个名为弗伦克尔 - 康托洛娃模型的简单非可积模型中热传导的近期研究工作。已发现该模型的热导率是有限的。我们将研究热导率对温度以及模型的其他参数（如外部势的强度和周期性）的依赖性。我们还将讨论其他相关问题，如相变和有限尺寸效应。热传导的研究不仅具有理论意义，也具有实际意义。我们将展示通过将非线性链耦合在一起而得到的热整流器和热二极管的各种近期设计。低维热传导的研究对于理解碳纳米管的热性质也很重要。
