A theoretical investigation of Zn?Zn and Be?Be one electron bond

Attachment of one electron to 1,2-diBeX-benzene and 1,2-diZnX-benzene derivatives leads to the formation of stronger Be Be and Zn Zn interaction compared to the neutral one. This is reflected in the dramatic shortening of the Be Be and Zn Zn distance. The formation of these 2-center-1-electron bonds have also been confirmed by topological survey of electron density using quantum theory of atoms in molecules and electron localization function. The formation of these bonds is expected to render stability to these radical anions. These radical anions are stable toward electron detachment and computed bond dissociation energy values are also significant.     

Geometric phase in a composite system subjected to decoherence

In this paper, we investigate the geometric phase of a composite system which is composed of two spin- particles driven by a time-varying magnetic field. Firstly, we consider the special case that only one subsystem driven by time-varying magnetic field. Using the quantum jump approach, we calculate the geometric phase associated with the adiabatic evolution of the system subjected to decoherence. The results show that the lowest order corrections to the phase in the no-jump trajectory is only quadratic in decoherence coefficient. Then, both subsystem driven by time-varying magnetic field is considered, we show that the geometric phase is related to the exchange-interaction coefficient and polar angle of the magnetic field.     

Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

Effect of disorders on topological phases in one-dimensional optical superlattices

In a recent paper, Lang et al. proposed that edge states and topological phases can be observed in one-dimensional optical superlattices. They showed that the topological phases can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions. However, disorders are not considered in their model. To study the effect of disorders on the topological phases, we introduce random potentials to the model for optical superlattcies.Our calculations show that edge states are robust against the disorders. We find the edge states are very sensitive to the number of the sites in the optical superlattice and we propose a simple rule to describe the relationship between the edge states and the number of sites. The density plateaus are also robust against weak disorders provided that the average density is calculated over a long interval. The widths of the plateaus are proportional to the widths of the bulk energy gaps when there are disorders. The disorders can diminish the bulk energy gaps. So the widths of the plateaus decrease with the increase of disorders and the density plateaus disappear when disorders are too strong. The results in our paper can be used to guide the experimental detection of topological phases in one-dimensional systems.     

Topological Invariants for Lens Spaces and Exceptional Quantum Groups

The Reshetikhin–Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras G2, F4 and E8 at odd roots of unity are constructed and explicitly computed for all the lens spaces.     

CH2XH→CH3X (X＝O, S, Se)异构化的量子拓扑研究

利用从头算和量子拓扑方法讨论了CH₂XH→CH₃X (X＝O, S, Se)异构化过程的反应机理. 着重从电子密度拓扑分析计算了反应进程中的各点, 讨论了反应进程中键的断裂和生成, 上述反应都经历了三元环过渡结构, 找到了这类反应的"能量过渡态"和"结构过渡态", 且结构过渡态均在能量过渡态之后出现. 三元结构过渡态结构出现的范围与反应热成正比.     

半Heusler型拓扑绝缘体LaPtBi能带调控的研究

采用基于密度泛函理论的全势能线性缀加平面波的方法, 研究了化学替代和施加等体积单轴(拉、压)应力两种方式对半Heusler型拓扑绝缘体LaPtBi能带的影响. 计算结果表明, 通过在LaPtBi合金中用Sc元素替换La, 或者用Pd替换Pt, 都可以使得原本受立方对称性保护的Γ₈能带在费米能级附近打开一带隙; 而对于施加等体积单轴应力来扭曲立方晶格的方式, 在使得Γ₈ 能带打开的同时, 还可以实现对费米能级位置有规律地调控, 使 LaPtBi合金最终成为真正意义上的体材料是绝缘性而表面是金属性的拓扑绝缘体.     

吡咯与HX(X=F,Cl,Br)分子间多种氢键的电子密度拓扑研究

采用密度泛函B3LYP/6-311＋＋G(d,p)方法, 对吡咯与HX (X＝F, Cl, Br)形成的经典氢键和π型氢键, 从其几何参数、电子密度的拓扑性质和电子积分等方面进行了研究. 在对π型氢键的讨论中我们将π电子与σ电子分离, 得到了π型氢键体系的π电子的密度等值线和拉普拉斯量等值线图以及各原子的π电子积分, 形象地说明了π型氢键的作用本质.     

平面连续体多工况应力约束下结构拓扑优化的有无复合体方法

本文在[4]的基础上,按“有无复合体”模型对应力的约束下多工况平面连续体结构拓扑优化的求解进行研究,提出了“工况影响系数”的概念,用于“病态荷载”问题的识别的解决,获得了令人满意的数值结果。     

多环涡旋光束的实验研究

涡旋光束的产生、传输与应用是当前光学领域热门的研究课题之一.本文提出的新型多环涡旋光束,包括双环涡旋及三环涡旋光束,它是由多束携带不同拓扑电荷数且束腰半径不同的拉盖尔-高斯涡旋光束共轴叠加而成,其光强分布为多环结构.从理论上研究了多环涡旋光束的形成与分布特征,基于共轭对称延拓Fourier计算全息方法生成了多环涡旋光束的计算全息图,并利用一个空间光调制器实验产生了与理论一致的高质量的多环涡旋光束.研究表明多环涡旋光束的各环携带不同的轨道角动量,空间分布保持相互独立.这种新型的多环涡旋光束相对于携带单一拓扑电荷数的涡旋光束,提供了更多的控制参数和更加多样化的结构分布,因此在光学镊子、光学捕获等微操控以及光通信领域具有潜在的应用潜力.