含复铰运动链同构及拓扑对称性判断的方法和程序

本文提出了便于计算机处理的运动链结构图的表示方法。以此为基础，利用邻接链表示法直接对含复铰或不含复铰运动链结构图进行同构或拓扑对称性判断，并用ＴｕｒｂｏＰｒｏｌｏｇ语言编制了相应的程序ＭＩＳＯＡＴ。从而成功地将这两种运动链的机构及拓扑对称性判断问题统一了起来，简化了此类问题的求解过程。

含复铰平面运动链拓扑对称性识别的邻接矩阵方法

提出了识别含复铰平面运动链拓扑对称性的邻接矩阵方法。根据能够反映复铰和多副杆特点的构件邻接矩阵和铰链点关联矩阵,按照构件或铰链点的划分,利用圆排列转动和圆排列对应匹配的方法进行构件或铰链点拓扑对称性的识别,并提出了基本算法。研究表明:该方法能应用于无复铰平面运动链,并且具有简便、直观、可靠和便于用计算机进行处理等特点。

含复铰平面开链和拓扑对称性在型综合中的应用

提出了在运动链型综合组合法中应用的含复铰平面开链的有关概念 ,给出了构造平面开链的方法 ,以及六杆以下所有的开链型式。同时 ,讨论了平面闭式运动链和平面开链中铰链点拓扑对称性的判断问题 ,给出了判断方法及其在型综合中的应用方法。研究表明 ,利用拓扑对称性可以有效地减少同构运动链型的数量。

一种运动链拓扑对称性识别方法

运动链拓扑对称性需要识别以减少机械装置新构型的备选方案,提高机械结构设计的效率。本文基于连杆邻接矩阵提出了一种新的运动链拓扑对称性识别方法。首先以连杆邻接矩阵为已知量导出汉明矩阵,计算汉明矩阵的平方阵与连杆邻接矩阵的立方阵,其次将上述平方阵与立方阵求积得积矩阵且将此积矩阵各行中的元素按降序排列得积矩阵行序列,最后将序列中各元素与拓扑因子相乘并求和得出运动链的拓扑对称性识别码(Topological symmetry recognition code,TSRC)。若同一拓扑图中两顶点的对称性识别码相同,则它们是对称的,否则是非对称的。通过单铰、复铰运动链和行星轮系的实例证明此方法的有效性,结果表明:此方法简单、高效且便于计算机编程。

视觉搜索中非对称性的实验研究

为了解视觉搜索中的非对称性现象以及封闭性这一拓扑特征在前注意加工中的作用,验证Treisman提出的特征整合理论,本实验对Treisma封闭圆开口圆靶子视觉搜索实验进行了改编,对视觉非对称性搜索的加工特征进行了验证研究。结果发现:对封闭圆的搜索时间显著大于开口圆的搜索时间,体现了视觉搜索的非对称性;开口圆的搜索不受开口大小的影响,开口大小对封闭圆视觉搜索时间的影响不明显;无论搜索开口圆还是封闭圆,画面大小都对其反应时有显著的影响,本研究结果证实了前注意加工阶段的存在及靶子和干扰项和互动关系。

Non-Hermitian pseudo-gaps

The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.

Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces

Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.

Superconductivity with two-fold symmetry in topological superconductor SrxBi2Se3

Topological superconductivity is the quantum condensate of paired electrons with an odd parity of the pairing function. By using a Corbino-shape like electrode configuration, we measure the c-axis resistivity of the recently discovered superconductor SrxBi2Se3 with the magnetic field rotating within the basal planes, and find clear evidence of two-fold superconductivity. The Lane diffraction measurements on these samples show that the maximum gap direction is either parallel or perpendicular to the main crystallographic axis. This observation is consistent with the theoretical prediction and strongly suggests that SrxBi2Se3 is a topological superconductor.

Detection of topological symmetry in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

A scheme is proposed for detection of the topology in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model,based on ultracold spinor atomic gas in an optical lattice.For this purpose,a global operation O(θ)is introduced with respect to the breaking of spinrotational symmetry.Consequently,the topology can be manifested unambiguously by identifying the special values ofθwhere the expectation value of the global operator with degenerate ground states is vanishing.Furthermore,experimentallyθcan be detected readily by the interference of ultracold atomic gases.This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.

Symmetry protected topological Luttinger liquids and the phase transition between them

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid.Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid.Both phases have full spin gaps and exhibit power-law superconducting pair correlation.The Cooper pair symmetry is singlet dxy in the non-trivial phase and triplet Sz? 0 in the trivial phase.The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary,and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned.As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes.We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.