拓扑材料中的超导

近来,人们在凝聚态体系中发现了由拓扑不变量定义的物相,其中最重要的有拓扑绝缘体、拓扑半金属和拓扑超导体等.这些物相的拓扑性质由非平凡的拓扑数描述,相应的材料被称为拓扑材料,具有诸多新奇的物理特性.其中拓扑超导体由于边界上有满足非阿贝尔统计的Majorana零能模,成为实现拓扑量子计算的主要候选材料.除了探索本征的拓扑超导体外,由于拓扑性质上的相似性,在不超导的拓扑材料中调制出超导自然成为了实现拓扑超导的重要手段.目前,人们发展了栅极调制、掺杂、高压、近邻效应调制和硬针尖点接触等多种技术,已经成功地在许多拓扑绝缘体和半金属中诱导出了超导,并对超导的拓扑性和Majorana零能模进行了研究.本文回顾了本征拓扑超导候选材料,以及拓扑绝缘体和半金属中诱导出超导的代表性工作,评述了不同实验手段的优势和缺陷、分析了其超导拓扑性的证据,并提出展望.     

Computing upward topological book embeddings of upward planar digraphs

We describe a unified approach for studying book, point-set, and simultaneous embeddability problems of upward planar digraphs. The approach is based on a linear time strategy to compute an upward planar drawing of an upward planar digraph such that all vertices are collinear. Besides having impact in relevant application domains of graph drawing and computational geometry, the presented results open new research directions in the area of upward planarity with constraints of the positions of the vertices.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.     

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R ⁿ ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. Project supponed in pan by the National h’atural Science Foundation of China (Grant No. 19131080) and the NEDF of China.     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications

In this note, we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way, the metric properties of the examined problem can be analyzed more precisely. Moreover, this approach allows us to derive from the same theorem, on the one hand, semilocal results of Kantorovich-type, and on the other hand, global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved, on the one hand, we cover a wider range of problems, and on the other hand, by choosing our operators appropriately, we can find sharper error bounds on the distances involved than before. Furthermore, we show that special cases of our results reduce to the corresponding ones already in the literature. Finally, several examples are being provided where our results compare favorably with earlier ones.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC