近年来，低维材料力热声光电特性的研究引起了人们的广泛关注。理解热传导和热 扩散在微电子及光电设备有着重要意义。然而，我们还不能够像电传导一样操控热传 导，由此引发了设计各种热设备操控热流，其中负微分热阻现象起着一个很关键的作 用。本文侧重于对负微分热阻现象进行分类，并讨论了另一种负微分热阻现象并用现有 手段理解和比较该现象。 第一章中，首先介绍了傅里叶定律以及反常热传导、非对称热传导和负微分热阻三 种反常现象，并对基本模型和概念，如热浴、温度、热流、热阻等进行定义和理解。 第二章中，重点介绍了负微分热阻现象的研究状况。发现均匀系统和非均匀系统均 能产生负微分热阻现象，而且产生方式是不一样的。关于产生的原因，均匀系统和非均 匀系统是不一样的，但也是众说纷纭，均匀系统或许是由于系统本身亦或是边界性质， 非均匀系统或许是功率谱的匹配/不匹配关系，或者是因为弹道输运和扩散输运的相变过 程，亦或是温度差和热阻的竞争等。同时介绍了理论上负微分热阻判据满足的条件。 第三章中，我们从热流和两端温度的三维图像出发，研究发现传统产生负微分热阻 现象的方式，通过固定一端温度改变另一端温度的方式只是众多产生方式中的一种观测 方法，对应着系统产生的一个过程，图像中的一个方向，即热流对温度的倒数。基于观 测方法将负微分热阻现象分成三类。同时给出了负微分热阻现象的自然表达、常规表达 和观测表达三种表达方式。一般的，第一类负微分热阻现象由均匀系统产生，第二类负 微分热阻现象由非均匀系统产生，除了一个特殊的四段耦合链构成的非均匀系统能够产 生两类负微分热阻现象。很自然的提出的一个疑问，为什么这特殊的非均匀系统也能产 生如均匀系统一样类型的负微分热阻现象呢？ 第四章中，我们主要将该特殊非均匀系统简化，单独研究非均匀系统是如何产生与 均匀系统一样的第一类负微分热阻现象。首先发现热阻和温度差的竞争关系可能是产生 负微分热阻现象的原因，而此时的热阻主要是由边界性质产生的界面热阻，当热阻起主 导作用时，出现温度差增加，热流减小的反常现象，而当温度差起主要作用时，出现正 常的现象。然后，将数值结果与通过负微分热阻产生判据所得临界温度差进行比较，发 现数值结果均在理论给出的范围内，并用热阻这一概念得到等价的判据和临界温度差。最后，发现成功解释小尺寸非均匀系统产生负微分热阻现象的功率谱匹配/不匹配的微观 机制并不适用于该系统。

The properties of low-dimensional materials in fields of mechanics, thermal, optical and electricity have attracted much attention in recent years. Understanding heat conduction and heat diffusion is of great importance in microelectricity and thermoelectricity. However, heat conduction can not be manipulated similarly to electric conduction. It has triggered designing various types of thermal devices controlling heat current. It is worth noting that, negative differential thermal resistance(NDTR) plays an important role in the operation of those devices. In this dissertation, we classify the phenomenon of NDTR and discuss another NDTR, then understand this phenomenon. In Chapter One, we firstly introduce Fourier law and three abnormal phenomena, i.e, abnormal heat conduction, asymmetric heat conduction, the NDTR. Then we define the basic model and concepts, including thermal bath, temperature, heat flux, thermal resistance. In Chapter two, we mainly introduce the research situation of NDTR. The homogeneous systems and inhomogeneous systems both can generate NDTR in different ways. It is inconsistent about potential reasons of generation NDTR in homogeneous and inhomogeneous systems. The homogeneous systems generate NDTR because of system itself or boundary property and the reasons of homogeneous systems may be the power spectrum match/dismatch, the transition from ballistic transport to diffuse transport or the competition between heat resistance and temperature difference. Then we briefly introduce the the general condition for the occurrence of NDTR. In Chapter three, we explore NDTR from a three-dimensional image. It is found that the conventional method of generating NDTR through fixing one temperature and changing the other to increase temperature difference just is one of the observation methods. It is corresponded to a process in system and a direction in graphic, namely the derivative of heat flux to temperature. NDTR are classified into three categories based on the observation method. At the same time, three expressions of natural expression, regular expression and observed expression of negative differential thermal resistance were given. In general, the first and the second category NDTR are produced by homogeneous system, inhomogeneous system, respectively, expect a special four-segment system generating two kinds of NDTR. A question naturally comes why this inhomogeneous system can generate the first category NDTR same as homogeneous system. In Chapter four, we mainly simplify the special four-segment system only studying the system how to generate the first category NDTR. The competition between thermal resistance and temperature difference is the potential reason generating NDTR. The thermal resistance mainly attribute to thermal boundary resistance due to boundary effects. When the thermal resistance dominates, the system appears the counterintuitive phenomenon of decreasing heat flux for increasing temperature difference. Reversely, when the temperature difference domains, the system appear normal phenomenon. Then we turn to the topic of compare numerical results of the temperature difference arising NDTR with the critical temperature difference by means of theoretically scaling analysis. It is found that numerical results are including in the range of theory and we also get a equivalent condition and critical temperature difference using the concept of thermal resistance. In addition, we also found the theory of power spectrum mitch/mismatch is not applicable to explain the microscopic mechanism for generating NDTR in our case although it is successful to reveal the mechanism for other small size composite systems.