Platonic Hyperbolic Monopoles

We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in ${\mathbb{R}^4}$ that are invariant under a circle action, and in most cases the monopole charge is equal to the instanton charge. A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance. Unlike for Euclidean monopoles, the formulae for the squared Higgs field magnitude in the examples we construct are rational functions of the coordinates. Using these formulae, we compute and illustrate the energy density of the monopoles. We also prove, for particular monopoles, that the number of zeros of the Higgs field is greater than the monopole charge, confirming numerical results established earlier for Euclidean monopoles. We also present some one-parameter families of monopoles analogous to known scattering events for Euclidean monopoles within the geodesic approximation.     

On axially-symmetric finite-energy monopole configurations

Axially symmetric finite energy monopole configurations are investigated for the gauge group SO(3) with the Higgs field in the adjoint representation. To avoid the complications due to gauge freedom gauge invariant fields are introduced and used throughout. From topological and continuity considerations it is argued that the only regular axially symmetric magnetic charge distributions permitted are isolated charges of uniform strength and alternate sign located along the axis of symmetry. In particular, if there is only one sign, the magnetic charge must be located at a single point. For a zero Higgs potential the minimal energy (first order Bogomolny) field equations take a simple form when written in terms of the gauge-invariant fields. In general, there are nine equations for nine (axially symmetric) fields, but these reduce to five equations for five fields if a further symmetry (invariance under reflexions in planes through the axis of symmetry) is imposed. Remarkably, four of the equations are the same whether the reflexion symmetry is imposed or not, and these four equations can be completely solved in terms of a master potential. From these and the remaining equations (just one in the case of mirror symmetry) the asymptotic behaviour of the functions at large distances and in the neighbourhood of the origin (the location of the charge) is obtained and studied in some detail.     

氦团簇及氦间隙原子在钨中的稳定性研究

首先采用分子动力学方法研究了在钨中预存氦-空位团簇（He_nV₂₂）后氦原子结合能与氦-空位比的关系。研究发现:当氦-空位比小于4.5时,氦原子结合能随氦-空位比呈线性减小趋势;当氦-空位比大于4.5时,氦原子的结合能随氦-空位比出现剧烈振荡的现象,这种现象是由于钨中预存氦-空位团簇随机挤出位错环使体系能量骤降所导致的。与此同时,氦-空位团簇周围出现了一些处于亚稳态的fcc结构和hcp结构的钨。为了研究氦团簇周围压强对钨基体相变的影响,本文利用第一性原理对钨的三种结构进行了高压相变计算,发现静水压力不能使钨的三种结构互相转变。另外,通过对bcc钨和fcc钨中四面体间隙氦原子和八面体间隙氦原子电荷密度差的计算,发现bcc钨中四面体间隙氦原子的稳定性高于八面体间隙氦原子的稳定性,而在fcc钨中四面体间隙氦原子的稳定性弱于八面体间隙氦原子的稳定性。     

Structural systematics in the family of (BEDT-TTF)2X salts

A crystallographic family tree can be developed for the (BEDT-TTF)₂X salts which aids in the systematization and rationalization of the structural and electrical properties of this novel series of materials. Importantly, it is recognized that the ambient-pressure superconductor α-(BEDT-TTF)₂I₃ has a crystal structure coincident with the parent subcell of this crystallographic family tree. Moreover, all first-generation supercells (doubling of any one subcell vector) are exclusively populated by salts with non-centrosymmetric anions of tetrahedral symmetry, and apparently, second-generation supercells (doubling of any two subcell vectors) are populated by salts with centrosymmetric anions of octahedral symmetry.     

Mössbauer studies and magnetic properties of spinel lead ferrite

In the present communication, we have reported the synthesis of nanocrystalline lead ferrite (PbFe₂O₄) by citrate mediated autocombustion method. X-ray diffraction pattern reveals the single phase formation in cubic (spinel) structure. The particle size and the surface morphology of the samples are characterized by TEM and SEM analysis. Magnetic studies are carried out using vibrating sample magnetometer (VSM) shows a very high coercive field for the material. Mössbauer studies were performed to investigate the local symmetry i.e. Fe is in octahedral/tetrahedral site and the charge states of Fe ions.     

Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

On a core instability of ''t Hooft–Polyakov type monopoles

We discuss a core instability of 't Hooft–Polyakov monopoles in Alice electrodynamics type of models in which charge conjugation symmetry is gauged. The monopole may deform into a toroidal defect which carries an Alice flux and a (non-localizable) magnetic Cheshire charge.     

Visualization of conduction channels and the dynamics of ion transport in superionic conductors

A method for visualizing conduction channels is proposed. This method is based on graphical analysis of conduction channel fragments which belong to a Voronoi-Dirichlet elementary polyhedron and lie outside the rigid sphere centered at a fixed-sublattice ion that is located at the geometric center of the elementary polyhedron under consideration. Taking into account the weak nonrigidity of spheres and root-mean-square displacements of ions in the fixed sublattice makes it possible to construct a channel as the surface of the mobile ion density. The most probable regions of mobile ion motion are quantum-mechanically interpreted as channel walls, which is confirmed by constructing the equipotential surfaces of interionic potential for α-AgI. It is found that the Andersson mathematical dynamics and the dynamics of ion transport in AgI lead to the same pattern of the motion. The symmetry rules are used for predicting the directions of motion along the allowed vibrational coordinates of tetrahedral and octahedral α-CuI fragments.     

Diffusivity and derivatives for interstitial solutes: activation energy,volume, and elastodiffusion tensors

Computational atomic-scale methods continue to provide new information about geometry, energetics and transition states for interstitial elements in crystalline lattices. This data can be used to determine the diffusivity of interstitials by finding steady-state solutions to the master equation. In addition, atomic-scale computations can provide not just the site energy, but also the stress in the cell due to the introduction of the defect to compute the elastic dipole. We derive a general expression for the fully anistropic diffusivity tensor from site and transition state energies, and three derivatives of the diffusivity: the elastodiffusion tensor (derivative of diffusivity with respect to strain), the activation barrier tensor (logarithmic derivative of diffusivity with respect to inverse temperature) and activation volume tensor (logarithmic derivative of diffusivity with respect to pressure). Computation of these quantities takes advantage of crystalline symmetry, and we provide an open-source implementation of the algorithm. We provide analytic results for octahedral–tetrahedral networks in face-centred cubic, body-centred cubic, hexagonal closed-packed lattices, and conclude with numerical results for C in Fe.     

Calculation of the muon polarization function for longitudinal fields

Fields for a muon interacting with a single nucleus is presented. The results demonstrate quantitatively the phenomenon of the level-crossing resonance between the muon Zeeman splitting and the induced quadrupolar coupling of neighboring nuclei. Approximate numerical solutions are given for the cases of a muon interacting with four (tetrahedral site) or six (octahedral site) Cu nuclei.     

单轴应变对H在α-Fe中占位及扩散的影响

采用基于密度泛函理论的第一性原理方法,研究了H在不同单轴应变下α-Fe中的间隙占位,计算了H原子的溶解能、态密度、电荷差分密度和电荷布居.结果表明:不同单轴拉压应变作用下,H原子优先占据四面体间隙(Ts)位,且随着压应变减小、拉应变增加,H原子越易溶于α-Fe.压应变使得Ts位的H获得更多的电子,而拉应变减少了这种电荷转移.应用LST/QST过渡态搜索计算垂直应变方向的扩散.八面体间隙位是邻近Ts位H的扩散过渡态.扩散激活能与应变呈线性关系,且随着压应变的增加,扩散激活能降低,扩散更容易.     

Orbital Precession Effect in the Reissner-Nordström Field with a Global Monopole

Using an elegant mathematical method advanced by us, we calculate the orbital precession effect in the gravitational field of the centre mass with electric charge and a global monopole. Analysing the results, we obtain that the orbital precession effect increases on account of the global symmetry breaking, but the orbital precession effect aroused by the electric charge of the field source reduces the orbital precession effect aroused by the mass of the field source. Generalizing the effect in the Schwarzschild field, we obtain interesting results by discussing the parameters of the celestial body, which provide a feasible experimental verification of the general relativity.     

Aharonov-Casher和He-McKellar-Wilkens相位的对偶对称关系

本文首先对电磁理论中的对偶对称性以及对偶变换做了简要回顾.然后讨论了与电磁相互作用相联系的Aharonov-Casher和He-McKellar-Wilkens相位之间的对偶对称性.最后,在宇称不守恒但具有相对论不变性的条件下,给出了一般情况下描述Aharonov-Casher和He-McKellar-Wilkens相位之间对偶对称关系的拉格朗日量,从而建立了统一的、不依赖于模型的描述Aharonov-Casher和He-McKellar-Wilkens相位之间对偶对称关系的方法.     

Low-symmetry spin hamiltonian and crystal field tensors analysis: Fe(3+) in natrolite

Electron paramagnetic resonance study of a natural single crystal of natrolite was carried out at the frequency nu=36.772 GHz at room temperature. The angular dependence of the four symmetry-related spectra of Fe(3+) in the three crystallographic planes was fitted to a spin Hamiltonian (S=5/2) of symmetry C(i). The rank 4 crystal field tensors at tetrahedral sites were calculated using the point-charge model to determine the principal axes orientations of their cubic and trigonal components. The analysis of zero-field splitting tensors and comparison with crystal field ones suggests that Fe(3+) substitutes for Al(3+) with no significant distortion of the coordination tetrahedron in natrolite. Comparison of data for several natural and synthetic crystals reveals that the 4-rank zero-field splitting tensor invariants for Fe(3+) at the tetrahedral oxygen-coordinated sites are distinguishably smaller than those for Fe(3+) at octahedral sites. Such comparative analysis may help to determine the substitutional sites in other crystals.     

基于壳模型对力加四极力研究sd和pf壳偶偶原子核

本文在原子核壳模型框架下基于唯象相互作用(对力加四极力)研究sd壳和pf壳的偶偶核低激发集体态。在提取了USDB和GXPF1相互作用的单粒子能量和单极相互作用的基础上,我们用一套统一参数计算重现了球形核和形变核的低激发谱;将对相互作用中的单极成分扣除后可以得到较好的结合能计算结果。同位旋标量的对相互作用对计算结果影响不大。单极相互作用在经验质子—中子相互作用、原子核对称能和Wigner能中产生重要贡献。     

Gravitationally bound monopoles

We construct monopole solutions in SU(2) Einstein-Yang-Mills-Higgs theory carrying magnetic charge n. For vanishing and small Higgs self-coupling, these multimonopole solutions are gravitationally bound. Their mass per unit charge is lower than the mass of the n = 1 monopole. For large Higgs self-coupling only a repulsive phase exists.     

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac’s quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.     

Atomic positions and diffusion paths of h and he in the α-Ti lattice

The solution energy of H and He in various interstitial and substitution positions in the hcp lattice of α-Ti has been calculated based on the method of electron density functional. The lowest solution energy of He corresponds to the basal octahedral position and that of H corresponds to the octahedral position (next in energy is the tetrahedral position). The calculated vibration frequencies of H in various positions are used for identification of lines in the vibration spectrum obtained by the method of neutron inelastic scattering. Taking into account these spectra, it can be concluded that hydrogen atoms occupy in the hcp lattice of Ti both the octahedral and tetrahedral positions even at 600 K. The available experimental data do not contradict the conclusion that the octahedral position is more preferable in α-Ti. The energy barriers are estimated for various diffusion paths of H and He.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.