本论文针对介观系统中的输运现象做了较为系统的理论研究。其目的在于揭示介观系统中的新效应的其物理机制，并为设计和实现具有优良性能的量子器件提供物理模型和理论依据。 首先, 为了更好地研究介观系统中的许多新问题，基于Dyson 方程，提出了一种广义的迭代格林函数方法，以适用于任意的边界条件和形状效应等具体问题。这是传统的迭代格林函数方法的一种推广, 具有普适性。 然后, 研究了量子点晶格中的一般输运性质以及电子间强关联相互作用的影响。指出了磁性杂质和温度效应对于电子输运的影响。更为重要的是，在强电子关联相互作用下，发现了这一体系中存在着金属----反铁磁绝缘体相变，指出了其本质原因是由于电子间的强关联相互作用使得体系形成了反铁磁态，从而阻碍电子的输运过程。这一相变发生在电子半填满的区域。同时，还指出了在小体系当中体系对称性对反铁磁态产生的影响。 还研究了一个带有量子点的介观环系统的电子输运性质。指出当量子点不处于共振隧穿态时，体系的电子输运性质由CP(环上除量子点以外的部分)的状态决定；而当量子点处于共振态时，体系的性质由共振隧穿和干涉效应共同表征。在紧束缚近似下的计算结果与实验符合很好。此外, 还用一个半经典的散射模型来研究了这一系统。由于采用了一个合适的散射矩阵来模拟环与外界连接的结点----点接触, 其结果与实验符合很好。在此基础上解析地分析了这一系统中的主要输运性质, 再一次证实了在这一系统中共振隧穿和干涉效应的主导作用。 最后, 研究了一个耦合双量子点系统，发现可以通过引入额外的耦合路径来仿真实际原子中的成键作用。在双向耦合的条件下，揭示出系统宇称对于电子态相互作用的影响，并给出了其对应的电子输运特性，为在实验上对这一系统的研究提供了理论依据。结果还表明，由于这一系统和分子的性质之间的很强的对应关系，实际上是构造了一个可控制和调谐其状态的“人造分子”。应用这个“人造分子”，人们可以研究在自然的分子中由于原子间相互作用不能直接控制而不能观测的特性，并给出原子间相互作用的更为深入的信息，为人们更好地了解分子间的成键作用提供实验依据。关键词： 介观系统，相变, 共振隧穿, 干涉效应, 人造分子答辩日期：1998年6月4日 指导教师签字：? 英文文摘

In this work we have made a detail investigation on the electronic transport properties through mesoscopic system. Our aim is to explore the physical mechanisms of the new effects in mesoscopic systems, and to supply physical models and make theoretical validity in designing novel quantum devices with better properties.First, A general recursive Green’s function method, which can be used for systems with arbitrary shapes and connection conditions in the same footing, is proposed based on the Dyson’s equation. It is a generalized method of the conventional recursive Green’s function method, and can be applied widely.Then, we study the general transmission properties and the effects of strong correlative interactions between electrons in a lattice of quantum dots. The effects of magnetic impurities and temperature on the transmission properties in this system are investigated. Moreover, it is found that there exists a metal to antiferromagnetic-insulator transition, which is driven by strong correlative interactions, around the half-filling in this system. Our numerical results explain, for the first time, that the Mott-insulator state is caused by the antiferromagnetic spin density wave.The resonant tunneling in an mesoscopic ring with a quantum dot embedded in one of its arms is also investigated. The system can be divided into two parts: the small dot and its big complementary partner (CP) which is attached by two ideal leads. A complete transmission mechanism, considering both the resonance of the dot and the interference effect, is presented. The transmission character is basically dominated by the CP when there is no resonance in the transmission through the dot. As a consequence, the experimental results, the phase features for conductance peaks, are well explained by an one-dimensional noninteracting model. Moreover, a semi-classical scatterer model is applied to study this system. With a proper scattering matrix, which describes the junctions between the leads and the ring, we show analytically that the quantum interference effects and the resonant tunneling through the quantum dot dominate the transmission. The dependence of the total transmission coefficient on the properties of the quantum dot is also presented and agrees well with the experimental results.Last, The properties of coupled quantum dots are studied theoretically. We find that by introducing multiple coupling paths, rather than the single tunneling path used in previous studies, the effects of bond direction on an artificial molecule can be simulated. The effects of parities of the orbits on the interactions between them are revealed. The electron transmission properties in this system is also given. Because the components of this molecule, coupled quantum dots, are controllable, this system is ideally suited for fundamental studies in a regime that is inaccessible on real atoms. Our study also examine the electronic transport property of the system, which could be checked experimentally. The system herein reported is both theoretically and experimentally interesting, not only because it is molecular-like, but also because it is a controllable system. Much novel information about molecules and the interactions among atoms may be revealed and used in further analysis and experiments.