微观体系中热传导的发散行为及其智能控制

When it comes to transporting energy, the heat conduction and electric conduction are two fundamental energy transport mechanisms of comparable importance, however the former one has never been treated equally in science, compared with the latter one. As the temperature in any material distributes non-uniformly, heat conduction appears, trying to pull the system back to equilibrium that is with uniform temperature distribution. In the cases that the temperature of a material is high beyond its Deby temperature, heat energy is basically stored in the oscillation of the particles of the crystal lattice. Heat conduction is also basically completed by the coupling of oscillating particles. The part of heat conduction that is by electrons is negligible. This project mainly concerns the physical underlying mechanism of heat conduction under these cases. Researches in the application aspect will focus on smart and functional control of heat flow in material in microscopic scale, including models of thermal diode, thermal transistor, thermal logic gates, etc and their possible experimental realization. These related works have been turning 'phononics', the new subject that based on thermal information independent process (without help of any electronic device) in microscopic scale, into reality. Therefore it is a topic full of challenges and potential applications. In the theoretical aspect, we will use molecular dynamics simulation and modern statistical physics as well as nonlinear dynamics, combined with the fundamental concepts and methods including the newly developed mode-coupling theory, hydrodynamical renormalization analysis and effect phonon theory etc. to analytically and numerically study the underlying mechanism of heat transport process, in particular the universality of the divergent exponents of abnormal heat conduction, and the correlation between super-diffusion and abnormal heat conduction. The studies will be conducted in both low dimensional models and high dimensional nonlinear systems that well describe real nano-scale materials such as nanotubes, nanowire etc. Those fundamental studies not only have their theoretical importance, but greatly help the studies in the applied researches as well.

热传导是自然界中和电传导同等重要的能量输运方式。然而对前者的研究却远不及后者。当材料中的温度分布不均时，热传导就会产生以试图使温度均匀分布达到热平衡状态。在材料的温度远高于其德拜温度时，热传导主要由粒子振动间的耦合完成。本项目主要研究在上述情况下热传导的特性行为。应用方面，研究工作集中于对微观材料中热流的精确智能控制，包括热二极管、热三极管等热控制模型的设计及实现。近期的相关研究已经使"声子学"这个基于微观尺度内热信息处理的新兴学科广受关注，成为一个富有挑战意义和实际应用价值的研究方向。理论方面采用分子动力学模拟，结合模耦合理论、重整化群理论、有效声子理论等基本概念和方法，系统研究低维和接近实际材料的高维非线性模型中热传导的发散机制，发散幂指的普适性，发散幂指和热能超扩散幂指的关联等一系列相关问题。这些基础问题不但具有理论上的重要性，对应用方面的研究也有重要的指导辅助作用。

本项目的研究主要在以下几个方面开展：（1）二维动量守恒系统中热传导的普适发散特征。研究确认了理论预期的对数发散，并指出了之前研究所得的偏离结果为有限尺度效应所导致。（2）一维动量守恒系统反常热导的确认。研究证明了非对称相互作用势导致的热导率平台现象是一种有限尺度效应，而在更大的尺度范围内热导率仍将如理论预期的一样以幂律发散。（3）在暂态热导方面研究了一系列一维晶格系统中的非稳态热导对Maxwell-Cattaneo定律的系统性偏离，更高阶的效应必须加以考虑以解释这些偏离。另外还有一个热二极管模型在周期温度驱动下的频率响应。各参数对频率响应的影响进行了详细计算。这些研究将有助于未来高速热二极管，热三极管等热控制器件的设计工作。（4）研究了应用Green_kubo公式计算热导率时的有限尺度效应，研究发现此效应对模型尺寸和关联时间都满足一个很好的幂律关系。数值远比传统预期为小，因此大大扩展了此公式的应用价值。（5）研究了超扩散和发散热导之间的关联性，发现之前学者提出的一个普适公式在含非对称相互作用系统中结果有所偏差。因此质疑了普适关联的存在。（6）研究了一个含外势作用的一维硬球模型中热和粒子的输运过程。研究发现在所有粒子质量相等的平庸情况下，系统热电转换效率的ZT值可以随模型参数的变化而迅速趋于无穷。而在非平庸的情况下ZT也可以随系统长度的增加以较慢的速度增加，且在外势高度很大时和其成正比增加达到很高的数值。这为高效热电材料的设计提供了理论支持。（7）基于线性响应理论提出了一个共振声子方法，此方法不仅计算简单而且相对于近期提出的非简谐声子方法本方法得到的色散关系与有效声子方法吻合得更好。方法的适用范围也大大扩展。不仅可用于更多的参数范围，更重要的是适用于双原子模型，可以直接得出含有清晰间隙的声子声学支和光学支。