Gauge cosmic chiral strings in general relativity

Cylindrically symmetric self-gravitating configurations of string (vortex) type are considered within the framework of the chiral SU(2) model with the inclusion of the Yang-Mills proper gauge field. In the approximation of the large topological charge n the solutions to the field equations are found, with the magnetic field of the vortex being longitudinal. The linear energy density of the vortex configuration is estimated. The text was submitted by the author in English.     

Chiral self-gravitating cosmic vortices

In the framework of general relativity, an exact axisymmetric (vortex) solution of the equations of motion is obtained for the SU(2) symmetric sigma model. This solution is characterized by the topological charge (winding number) and angular deficit. In the linearized approximation, the Lyapunov stability of vortices is proved and the deflection angle of a light ray in the gravitational field of the vortex (gravitational lens effect) is calculated.     

Skyrme-Einstein closed cosmic chiral strings

Within the theory of general relativity, the configuration of a closed string (vortex) characterized by a topological charge of the degree type is described for the Skyrme-Einstein SU (2) chiral model. In the approximation of a large vortex-closure radius (a), a solution to equations of motion is obtained, along with estimates for the vortex energy and radius.     

Angular momentum density of a Gaussian vortex beam

The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.     

Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields

We study the phase-space properties of a charged particle in a static electromagnetic field exhibiting vortex pairs with complementary topological charges and in a pure gauge field. A stationary solution of the Schrödinger equation that minimizes the uncertainty relations for angular momentum and trigonometric functions of the phase is obtained. It does not exhibit vortices and the angular momentum is due to the gauge field only. Increasing the topological charge of the vortices increases the regions where the Wigner function in the angle–angular momentum plane takes negative values, and thus enhances the quantum character of the dynamics.     

涡旋洛伦兹-高斯光束的远场矢量结构特征

利用矢量角谱法和稳相法,研究了涡旋洛伦兹-高斯光束的远场矢量结构特征,导出了横电项(TE项)和横磁项(TM项)远场电磁场和相应能流的解析表达式。通过相应的数值计算,分析了拓扑电荷数对涡旋洛伦兹-高斯光束及其矢量结构项远场能流分布的影响。TE项由位于竖直方向的2瓣或3瓣组成,TM项可由TE项旋转90得到。涡旋洛伦兹-高斯光束在拓扑电荷数小时内部中空,外部亮环均匀分布。增大拓扑电荷数,涡旋洛伦兹-高斯光束外部亮环上的能流呈起伏分布,内部变化相对复杂。涡旋洛伦兹-高斯光束及其矢量结构项的光斑尺寸随拓扑电荷数的增大而增大,但会饱和。研究显示,涡旋洛伦兹-高斯光束在实际应用时拓扑电荷数不宜过大。     

Rotating vortex dipoles in ferromagnets

Vortex-antivortex pairs are spontaneously created in magnetic elements. In the case of opposite vortex polarities the pair has a nonzero topological charge, and it behaves as a rotating vortex dipole. We find theoretically and confirm numerically its energy as a function of angular momentum and the associated rotation frequencies. The annihilation process of the pair changes the topological charge while the energy is monotonically decreasing. The change of topological charge affects the dynamics profoundly. We finally discuss the implications of our results for Bloch point dynamics.     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle

We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an airglass interface near the Brewster angle.A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle.Using a hybrid angular spectrum representation and vector potential method,the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation.The local energy,momentum,spin,and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach.Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly,and are significantly affected by their topological charge,half-cone angle,and polarization state.The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.     

单环多段光强分布检测光学涡旋拓扑荷值

针对涡旋光束检测范围局限这一问题, 提出了一种新的光学涡旋拓扑荷值检测方法-单环多段光强分布检测法, 它以分段数和环半径为两大检测常数, 将检测涡旋光束拓扑荷值范围扩大到了128种, 与以往利用旁瓣调控光学涡旋检测拓扑荷值方法相比, 检测范围扩大了1个数量级. 单环多段光强分布是基于计算机全息图实现在远场衍射焦平面上环半径相等的两束携带不同拓扑荷数的涡旋光束叠加后形成的光强分布. 计算机模拟和光学实验验证了所提出方法的可行性, 该方法在自由空间光通信领域具有一定的研究价值和应用潜力.     

Tightly Focusing of Circularly Polarized Vortex Beams through a Uniaxial Birefringent Crystal

Under the approximation of small birefringence, the properties of circularly polarized vortex beams tightly focused through a uniaxial birefringent crystal are studied. With the proper combination of the topological charge and the birefringence, the small focus, the small bottle beam and the inverse c-shaped intensity profile can be obtained. The effects of the focal shift and the Strehl ratio on the birefringence are analysed. A relation between angular momentum （included spin and orbital） and topological Pancharatnam charge is also presented.     

TWO-DIMENSIONAL ANGULAR MOMENTUM AND FERMION IN THE FIELD OF MAGNETIC-FLUX-TUBE

In this paper, we showed that the eigenvalues of two-dimensional angular momentum of a particle with charge a are integer valued. The problems of a Dirac particle in a field of vortex were discussed. When the vortex tends-to string, we found that the system admits of the existence of θ vacua. For massless fermions, a change in θ is equivalent to a Γ_s rotation, while the physical result is independent of θ. For massive fermions, CP invariance is broken except for θ=0,π; and the system exhibits the Witten effect.     

Dynamics of magnetic vortices

The canonical conservation laws of linear and angular momentum in the ferromagnetic continuum have been known to be plagued by certain ambiguities which are resolved in this paper by constructing conservation laws as suitable moments of a topological density. The resulting canonical structure is then shown to be analogous to that encountered in the familiar Hall effect and explains the unusual features of the dynamics of magnetic vortices without resorting to a detailed solution of the underlying nonlinear equations. Thus, in the absence of external magnetic fields, a magnetic vortex is shown to be spontaneously pinned around a fixed guiding center. The guiding center would drift in a direction perpendicular to an applied magnetic field gradient, provided that dissipation can be neglected, with a Hall velocity that is calculated explicitly in terms of the initial configuration of the vortex. In the presence of dissipation, the vortex undergoes skew deflection at an angle δ ≠ 90° with respect to the applied field gradient. The angle δ is related to the winding number of the vortex according to the well-known golden rule of bubble dynamics.     

Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.     

Transfer of angular momentum to matter from acoustical vortices in free space

An experimental demonstration of the mechanical transfer of orbital angular momentum to matter from acoustical vortices in free field is presented. Vortices with topological charges l=+/-1 and l=+/-2 were generated and a torsion pendulum was used to study the angular momentum transfer to hanging disks of several sizes. This allowed us to make a comparative study of the effective acoustical torque in terms of topological charge of the vortex, the disk radius, and its position along the main propagation axis. A theoretical discussion of the generated sound fields is also provided.     

Mass of the higgs versus fourth generation masses

Double sign inversion of the topological charge of an optical vortex was predicted and observed experimentally for a beam focused by a cylindrical lens. Beam evolution after passing through the lens is analyzed by the decomposition of the orbital angular momentum into the “vortical” and “mechanical” components. Topological reactions in the beam wave resulting in the sign inversion of the optical vortex upon the intersection of the wave-front edge dislocation are considered.     

非相对论Chern-Simons多涡旋解的拓扑结构(英文)

运用规范势分解理论研究了Jackiw Pi模型中的自对偶方程, 得到一个新的自对偶方程, 发现了Chern Simons多涡旋解与拓扑荷之间的联系。为了研究Jackiw Pi模型多涡旋解的拓扑性质, 构造了一个新的静态自对偶Chern Simons多涡旋解,每个涡旋由5个实参数描述。 2个实参量用来描述涡旋的位置, 2个实参量用来描述涡旋的尺度和相位, 还有一个实参量描述涡旋的荷。 为了研究拓扑数对涡旋形状的影响, 给出了具有不同拓扑数的多涡旋解。 另外还研究了该涡旋解的磁通量的拓扑量子化。     

Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Dipole soliton-vortices

On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.