电磁场的复张量表述

在电磁场的三维复矢量表述基础之上获得对应的四维复张量表述形式,同时又考虑磁荷流密度并引入双势法,将电磁场复张量表述推广到同时包含电荷与磁荷流密度的情形并获得了复张量麦克斯韦方程组.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Effects of oxygen-containing defect complex on the electronic structures and transport properties of single-walled carbon nanotubes

The electronic structures and transport properties of (10,0)$(10,0)$ single-walled carbon nanotube ((10,0)$(10,0)$ (SWNT)) with oxygen-containing defect complex are investigated using density functional theory in combination with nonequilibrium Green?s function method. The complex delocalizes the local states of (10,0)$(10,0)$ SWNT induced by mono- and di-vacancy but strengthens the localization of the states induced by the Stone–Wales defect. As a result, the complex partially restores the transport properties of (10,0)$(10,0)$ SWNT with vacancies, but reduces the transmission of (10,0)$(10,0)$ SWNT with Stone–Wales defect. However, the oxygen-containing defect complex only slightly influences the transmission gap and threshold voltage of the system.     

基于低阶矩阵最大特征值的复杂网络牵制混沌同步

虽已对复杂网络牵制同步需要牵制结点数量及牵制结点数量与耦合强度的关系进行了研究,然而快速计算牵制结点数量仍是大规模复杂网络面临的一个重要问题.研究发现了复杂网络耦合矩阵主子阵最大值递减规律,由此提出了快速计算复杂网络牵制结点数量的方法,揭示了不同的牵制策略与牵制结点数量之间的关系.数值仿真显示了在无标度网络和小世界网络上三种不同的牵制策略下,牵制结点数与主子阵最大特征值的变化规律;最后给出了一个在无标度网络上采用随机选择结点策略的牵制同步实例.     

噪声诱导的二维复时空系统的同步研究

研究了一类噪声诱导的二维复时空系统的同步问题.首先讨论了二维复Ginzburg-Laudau(CGL) 方程随时间和空间变化的时空混沌特性;其次,研究了时空噪声驱动下CGL系统的同步问题.理论上利用线性稳定性分析,得到了常数激励下CGL系统达到稳定态的临界强度;结合噪声的随机性和非零均值特性, 揭示了噪声诱导同步的机理;并从理论上和数值上分别给出了达到同步所需要的控制参数和噪声强度满足的条件,实现了两个非耦合CGL系统的完全同步.结果表明,数值模拟和理论分析有很好的一致性.     

Effects of Some Topological Ingredients on the Evolutionary Ultimatum Game

This study aims at figuring out the crucial topological ingredients which affect the outcomes of the ultimatum game located on different networks,encompassing the regular network,the random network,the small world network,and the scale-free network.With the aid of random interchanging algorithm,we investigate the relations between the outcomes of the ultimatum game and some topological ingredients,including the average range,the clustering coefficient and the heterogeneity,and so forth.It is found that for the regular,random and small-work networks,the average range and the clustering coefficient have evident impacts on the ultimatum game,while for the scale-free network the original degree heterogeneity and the underlying rich-club characterizations are the mainly important topologica ingredients that influence the outcomes of ultimatum game substantially.     

结构与参量不确定的网络与网络之间的混沌同步

进行了结构与参量不确定的网络与网络之间的混沌同步研究．通过设计适当的控制输入,不但实现了两个复杂网络之间的混沌同步,而且网络节点状态方程中的未知参量和网络内部节点之间的耦合强度也被同时确定．通过采用具有调制损耗的CO2激光器的状态方程进行仿真实验,发现网络与网络之间的同步性能非常稳定．     

拉曼光谱法研究纳米结构多孔ZnO微球的合成机理

利用拉曼光谱方法,对柠檬酸钠辅助水热合成纳米结构多孔ZnO微球的机理进行了研究。样品的拉曼光谱特征显示,多孔ZnO微球中存在Zn-柠檬酸配合物;分析表明反应溶液中柠檬酸钠水解产生的柠檬酸根与Zn2+结合形成Zn-柠檬酸配合物,该配合物化学吸附在Zn(OH)₂晶核的(204)和(503)晶面,使Zn(OH)₂晶核择优生长形成纳米薄片状结构;水热过程中Zn(OH)₂微晶团聚形成纳米片状结构多孔Zn(OH)₂微球并以沉淀析出。研究发现吸附在薄片表面的Zn-柠檬酸配合物提高了Zn(OH)₂微晶的热稳定性,使得Zn(OH)₂的分解温度高于200 ℃,加热到300 ℃后Zn(OH)₂完全分解获得纳米结构多孔ZnO微球。     

金融动力学的时空关联与大波动特性——兼谈中西方金融市场的对比研究

文章扼要地评述了金融物理学研究进展,介绍了文章作者在金融动力学时空关联方面的最新研究成果,特别关注中西方金融市场的对比研究.唯象理论研究表明,西方金融市场的价格收益率和波动率的时间关联显示杠杆效应,而中国金融市场则显示反杠杆效应;一种价格收益率和波动率的反馈相互作用可以解释杠杆和反杠杆效应的起源.西方金融市场的个体股票价格的交叉关联呈现标准的行业板块结构,而中国金融市场展示的是一种特殊的板块结构,如"ST板块"和"蓝筹板块"等.股票价格大波动可分为动力学内部产生的和外部事件诱导的两大类.金融动力学的时间反演不对称性,主要来源于外部事件诱导的大波动.     

Complex Wave Solutions for （2＋1）-Dimensional Modified Dispersive Water Wave System

The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the （2＋1）-dimensional modified dispersive water-wave （MDWW） system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave.