中文摘要：

散射矩阵是刻画许多满足量子相干性介观体系的电子输运性质的重要理论工具．结合几个介观体系的量子力学散射问题，讨论了体系的对称性对散射矩阵对称性的重要影响．几个被讨论的例子包括：1）满足时间反演不变性的自旋轨道耦合体系；2）含单轴应变的石墨烯（满足中心反演对称）体系；3）含有Majorana费米子（手征Majorana粒子的一维波导模式或Majorana束缚态）的2个典型问题．从系统的对称性推导散射矩阵的对称性，进而对体系的输运性质得出一些定性的理解．在某些场合，依据散射矩阵的对称性甚至可以对体系的电子结构的拓扑性质给出预言．

英文摘要：

Taking scattering matrix as an important theoretical tool for characterizing the transport property of mesoscopic systems with quantum coherence, it was discussed the quantum scattering problem for several me-soscopic systems, which included ： 1 ） spin-orbital coupled systems with time reversal symmetry ; 2 ） graphene with ＇uniaxial strain which preserves inversion symmetry; 3）two typical problems related to Majorana Fermion （Chiral Majorana Fermion and Majorana bound states）. The symmetry property of scattering matrix from the symmetry of the system was deduced, and some qualitative understanding of the transport property were ob-tained. It was also pointed out that in some cases, even topological properties of electronic structure of the sys-tem could be predicted.