动量守恒的一维体系的热能输运

Fourier’s law is a fundamental law for physics, and has been widely accepted since it has been confirmed experimentally two hundred years ago. However, it is still an open and debated question whether Fourier’s law valid in low dimensional nanoscale materials. Since the characteristic length of phonon, which is the main heat carrier, is comparable to the characteristic length of nano-materials. The thermal properties of nano-materials are significantly different from bulk material. In some structures of nanomaterial, the thermal conductivity diverges as the length increases, where the Fourier’s law breaks down. Therefore, further investigation of the physical mechanism behind the Fourier’s law is timely and highly needed. Some numerical simulation and theoretical analysis show that the thermal conductivity diverges for the momentum-conserving system. However, there is still debate about the thermal conduction in 1D coupled rotator lattice, in which the momentum is conserved. Taking 1D momentum-conserving coupled rotator as an example, we will focus on the following parts: (1) For the low dimensional momentum-conserving case, why the energy diffusion process is normal diffusion in some system, and anomalous diffusion in others? (2) the relation between the thermal conductivity and the temperature; (3) Is there a phase transition? Since the typical methods to calculate the thermal conductivity are not so precise for large size system, new methods are needed to numerically and theoretically study the thermal diffusion in low dimensional system.

傅里叶定律是物理中一个非常重要的定律，至200年前被实验证实后，得到了广泛应用。但是对于最近广泛研究的低维纳米材料，傅里叶定律是否成立却存在着很多的争议。由于低维纳米材料与热传导的主要载体，声子的特征长度在一个数量级，所以表现出很多奇特的热传导性质。在有些材料中，热传导系数会随着材料的增大而发散，即不遵守傅里叶定律。因此进一步研究傅里叶定律的内在机制是目前值得开展的前沿性问题。目前的数值模拟和理论分析表明动量守恒系统，热传导系数发散，但是在动量守恒的一维耦合转子模型中，却存在争议。我们将以一维耦合转子模型为例来探讨以下3方面的内容：（1）为什么低维动量守恒系统中的能量扩散有的是正常扩散，有的是反常扩散？（2）热传导系数与温度的关系（3）是否存在相变现象。由于用目前的一般方法很难准确的计算较大尺度的热传导系数，因此我们将应用新的方法,从数值，解析分析方面，来深入研究热能在低维系统中的扩散机制

傅里叶定理在低维纳米材料中是否仍然成立，目前还存在着争议。由于热传导的主要载体，声子的特征长度也在纳米尺度，因此热传导性质表现出很多奇特的现象。在以前工作的基础上，这一年来我们重点研究了热传导性质与能量，动量扩散之间的关系，从动力学方程出发，发现能量（动量）扩散的性质与热传导的性质具有一致性，我们测试了不同的模型，验证了我们的结论。这个工作目前还在审稿过程中。预计2015年能够发表出来。我们的工作从理论方面，证实了可以通过研究能动量扩散性质来研究热传导性质，提供了一种更简洁的方法来判定是否是正常热传导。同时，我们还研究了双面粒子的输运性质，研究成果已经发表在Phys. Rev. E 90, 062301(2014), Europhys. Lett. 109,10003(2015) 及综述文章Eur. Phys. J. Special Topics 223, 3227-3242 (2014),详见附件论文。