Riemann-Hilbert problems for the Ernst equation and fibre bundles

Riemann-Hilbert techniques are used in the theory of completely integrable differential equations to generate solutions that contain a free function which can be used at least in principle to solve initial or boundary-value problems. The solution of a boundary-value problem is thus reduced to the identification of the jump data of the Riemann-Hilbert problem from the boundary data. But even if this can be achieved, it is very difficult to get explicit solutions since the matrix Riemann-Hilbert problem is equivalent to an integral equation. In the case of the Ernst equation (the stationary axisymmetric Einstein equations in vacuum), it was shown in a previous work that the matrix problem is gauge equivalent to a scalar problem on a Riemann surface. If the jump data of the original problem are rational functions, this surface will be compact which makes it possible to give explicit solutions in terms of hyperelliptic theta functions. In the present work, we discuss Riemann-Hilbert problems on Riemann surfaces in the framework of fibre bundles. This makes it possible to treat the compact and the non-compact case in the same setting and to apply general existence theorems.     

Symmetry and general symmetry groups of the coupled Kadomtsev--Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.     

准坐标下一般完整系统的统一对称性

研究准坐标下完整力学系统在时间不变的无限小变换下的统一对称性. 列出系统的运动微分方程, 给出系统的统一对称性的定义和判据, 由系统的统一对称性导出Noether守恒量、Hojman守恒量和一类新型守恒量. 举例说明结果的应用. 关键词： 准坐标 完整系统 统一对称性 守恒量     

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E((B, V, A) associated to a quantum principal bundle P (B, A) are in bijective correspondence with equivariant maps V → P, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with Ad_R-covariant maps A → P.     

It's the coupling that creates resistance: Spin electronics in layered magnetic structures

Fast‐paced technological advancement is squeezing the data on computer hard disks ever closer together. For some ten years now, continuously shrinking and increasingly sensitive read/write heads are making use of the giant magnetoresistance (GMR) effect discovered in 1988. This term was coined for the effect that electric resistance of a magnetic layer system changes dramatically when the magnetization of the individual layers is reversed from antiparallel to parallel orientation. Very small external magnetic fields suffice to change the orientation and thus give GMR read/write heads their high sensitivity.     

Majorana neutrino transition magnetic moment in a variant of Zee model with horizontal symmetry

A SU(2) _H symmetric variant of Zee model of lepton flavor violation is presented and is shown to lead to neutrino transition magnetic moment of the order required to explain the solar neutrino deficit and the possible anticorrelation of solar neutrino flux with sunspot activity via VVO mechanism. The use of horizontal symmetry leads to totally degenerate neutrino states which may be combined to form a ZKM Dirac neutrino with naturally small mass.     

带有附加项的广义Hamilton系统的Mei对称性

研究带附加项的广义Hamilton系统的Mei对称性的定义和判据，给出系统Mei对称性为Lie对称性的充分必要条件. 通过Lie对称性间接导出具有Mei对称性且带有附加项的广义Hamilton系统运动微分方程的Hojman守恒量. 举例说明结果的应用. 关键词： 附加项 广义Hamilton系统 Mei对称性 Hojman守恒量     

Discrete accidental symmetry for a particle in a constant magnetic field on a torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the 1/r and r² potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the θ-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters θ_x and θ_y explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.     

First-principles prediction of spin-density-reflection symmetry driven magnetic transition of CsCl-type FeSe

Based on results of density functional theory (DFT) calculations with the local spin density approximation (LSDA) and the generalized gradient approximation (GGA), we propose a new magnetic material, CsCl-type FeSe. The calculations reveal the existence of ferromagnetic (FM) and antiferromagnetic (AFM) states over a wide range of lattice constants. At 3.12 Å in the GGA, the equilibrium state is found to be AFM with a local Fe magnetic moment of . A metastable FM state with Fe and Se local magnetic moments of 2.00 and , respectively, lies 171.7 meV above the AFM state. Its equilibrium lattice constant is ∼2% smaller than that of the AFM state, implying that when the system undergoes a phase transition from the AFM state to the FM one, the transition is accompanied by volume contraction. Such an AFM-FM transition is attributed to spin-density z-reflection symmetry; the symmetry driven AFM-FM transition is not altered by spin-orbit coupling. The relative stability of different magnetic phases is discussed in terms of the local density of states. We find that CsCl-type FeSe is mechanically stable, but the magnetic states are expected to be brittle.     

Polarization properties of elliptical core non-hexagonal symmetry polymer photonic crystal fibre

In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding $\eta$ from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.     

强磁场对Al-Si合金凝固组织中硅分布的影响

为了揭示强磁场对金属凝固组织的影响规律，本文研究了Al-14.98%Si(质量分数)和Al-9.2%Si(质量分数)合金在强磁场作用下凝固组织的变化趋势，分析了强磁场对合金凝固组织中Si分布的影响.研究发现，均恒磁场和梯度磁场分别通过洛伦兹力和磁化力的作用对合金的凝固组织产生影响，强磁场可以显著改变初晶硅在合金中的分布状况.在均恒磁场作用条件下初晶硅在合金中均匀分布；在梯度磁场条件下，由于磁化力和浮力的共同作用，初晶硅在试样的上部或下部聚集.同时，磁化力也改变了共晶体在合金中的组织形态，使试样上部和下部共晶体的层片间距明显不同.理论和实验分析表明，Al-Si合金在强磁场中凝固时，磁场能作用于凝固过程，使共晶体中的Al含量增大，共晶点向左偏移. 关键词： 强磁场 凝固过程 共晶组织 Al-Si合金     

参杂GaAs量子点的电子结构

用有效质量近似和少体物理方法计算了在抛物势中,参杂（一个带正电荷）GaAs量子点中有7个极化电子时的本征能量和本征波函数,并从本征波函数中提取的一体、二体密度函数方法得到了电子结构的直观图像,用对称性对量子点中库仑相互作用能和电子结构进行了分析。     

磁性材料的磁结构、磁畴结构和拓扑磁结构

首先简要地介绍了磁性材料中磁结构、磁畴结构和拓扑磁结构以及相互之间的关系. 一方面, 磁畴结构由材料的磁结构、内禀磁性和微结构因素决定; 另一方面, 磁畴结构决定了材料磁化和退磁化过程以及技术磁性. 拓扑学与材料物理、材料性能的联系越来越紧密. 最近的研究兴趣集中在一些拓扑磁性组态, 如涡旋、磁泡、麦纫、斯格米子等. 研究发现这些拓扑磁结构的拓扑性质与磁性能密切相关. 然后从尺寸效应、缺陷、晶界三个方面介绍国际学术界在磁结构、磁畴结构和拓扑磁结构方面的进展. 最后介绍了在稀土永磁薄膜材料的微观结构、磁畴结构和磁性能关系、交换耦合纳米盘中的拓扑磁结构及其动力学行为方面的工作. 通过对文献的评述, 得到以下结论: 开展各向异性纳米复合稀土永磁材料的研究对更好地利用稀土资源具有重要的意义. 可以有目的地改变材料的微结构, 可控地进行磁性材料的磁畴工程, 最终获得优秀的磁性能. 拓扑学的概念正在应用于越来越多的学科领域, 在越来越多的材料中发现拓扑学的贡献. 研究磁畴结构、拓扑磁性基态或者激发态的形成规律以及动力学行为对理解量子拓扑相变以及其他与拓扑相关的物理效应是十分重要的. 也会帮助理解不同拓扑学态之间相互作用的物理机制及其与磁性能之间的关系, 同时拓展拓扑学在新型磁性材料中的应用.     

具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)_L×SU(2)_R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下, 关键词： 中微子质量 轻子味混合矩阵 左右对称模型 代对称性     

Electronic and magnetic structures of ternary iron telluride KFe2Te2

We examine the electronic and magnetic structures of iron telluride KFe₂Te₂ using first-principle calculations. We demonstrate that the ground state of this compound is in bicollinear antiferromagnetic order with Fe local moments (~ 2.6 μ_B) that are ferromagnetically aligned along a diagonal direction and antiferromagnetically aligned along the other diagonal in the Fe-Fe square lattice, similar to the alignment discovered in the parent compound of superconductor α-FeTe. This bicollinear antiferromagnetic order results from the interplay among the nearest, next-nearest, and next-nextnearest neighbor exchange interactions, which are mediated by Te 5p orbitals. This finding may aid our understanding of the interplay between magnetism and superconductivity in the family of iron-based materials.     

A New type of conserved quantity deduced from Mei symmetry of nonholonomic systems in terms of quasi-coordinates

This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system's results.     

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

Using the Bogoliubov inequality, we extend previously known results concerning the absence of continuous symmetry breakdown for equilibrium states of certain quantum and classical lattice, and continuum systems in two space dimensions.Partially supported by the N.S.F. under grant MCS 7801433.Partially supported by the N.S.F. under grant MCS 7906633.     

Broken relativistic symmetry groups,toroidal moments and superconductivity in magnetoelectric crystals

Summary A connection between the creation of toroidal moments and the breaking of the relativistic crystalline group associated to a given crystal is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, a Goldstone boson responsible for the production of toroidal moments is created and, consequently toroidal phases arise in the crystal. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.     

两种均匀磁介质分界面上有长载流导线的场和电流分布

分析两种均匀磁介质分界面上有长载流导线的场和电流分布，指出磁感应强度B=B(r)φ径向对称分布是由径向对称分布的总电流j=j(r)ez(包括传导电流和磁化电流)所激发,探讨了传导电流的分布与磁感应强度B、磁场强度H和磁化电流的分布的关系。     

稀磁半导体(Ga1-xFex)As的电子结构,磁性及其稳定性的第一性原理研究

采用基于第一性原理的紧束缚近似线性muffin-tin轨道(TB-LMTO-ASA)的方法,在原子球近似的基础上计算了均匀掺杂的稀磁半导体(Ga1-xFex)As在各掺杂浓度下(x=1,1/2,1/4和1/8)的总能量,由能量最低原理得到其在各稳定点的晶格常数,磁性及相应态密度.计算结果表明了(Ga1-xFex)As的晶格常数随掺杂浓度的增大而减小,在各掺杂浓度下(除x=1)样品都是反铁磁态的,Fe 3d和As 4p之间杂化是引起样品电子结构和磁性变化的主要原因.