准周期链状聚合物电子谱及特征

研究了链状聚合物的长短键结构呈准周期排列的电子谱。利用紧束缚近似和转移矩阵方法通过理论证明和计算表明：这种准周期排列聚合物的电子谱,当长短键长度相差很小时,具有类似于金属晶体的能带结构;相差很大时,具有无序系统一维能级结构;而对于一般情形,其电子谱与上两者均异,形成所谓的类Cantor集。这3类不同的谱结构反映在链状聚合物的宏观物理性质上也将有所不同,它无疑会影响聚合物的稳定性及相关(超)导电性能,深入研究这方面问题将有助于对有机超导的认识。     

二维晶格上Kadanoff分块及重整化群方法

对二维晶格上的Kadanoff分块进行了全面分析，给出了划分的一般规律，得出元块选择的非任意性和含相同元块选择不惟一等结论，并给出正三角形格子和正方形格子元块中格点数目的允许值。同时，利用重整化群方法对9点，13点元块进行了计算，得到了相应的不动点和各种临界指数，并与其它计算结果进行了比较，结果表明，计算精度有随元块中所含格点数的增加而增加的趋势。     

Linear and Nonlinear Optical Properties of Quasicrystals

An investigation is carried out on the linear and nonlinear optical properties of quasicrystaJs. The linear and nonlinear susceptibilities are determined for two- and three-dimensional ctuasicrystals. The results show that for optical linearity, two-dimensional quasicrystals are uniaxial, while icosahedral quasicrystals are optically isotropic. Meanwhile all ctuasicrystals, except those with 5, 5m, N, Nmm (N = 8, 10, 12) symmetries, have no the firstorder optical nonlinearity. The tensor scheme of the first order nonlinear susceptibility is the same for these eight exceptional kinds of quasicrystals.