Sharp existence and uniqueness theorems for non-Abelian multiple vortex solutions

Vortices in non-Abelian gauge field theory play essential roles in the mechanism of color confinement and are governed by systems of nonlinear elliptic equations of complicated structure. In this paper, we present a series of sharp existence and uniqueness theorems for multiple vortex solutions of the non-Abelian BPS equations over R²${\mathbb{R}}^2$ and on a doubly periodic domain. Our methods are based on calculus of variations which may be used to analyze more extended problems. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are expressed in terms of physical parameters involved explicitly.     

混合层流场中涡结构对流速度的特性

基于大涡模拟和光线追踪方法, 对光线穿越流场后的光程分布与混合层流场中涡结构之间的关系进行了分析, 提出了一种基于涡核位置提取的涡结构瞬时对流速度定量计算方法, 并使用直接几何测量数据进行了验证. 通过对不同尺寸的涡结构、涡-涡配对及融合过程中的涡结构和强压缩性流场中涡结构瞬时对流速度的定量数值计算, 揭示了混合层流场中涡结构对流速度的特性: 对单个涡结构而言, 其瞬时对流速度具有脉动特性, 且脉动幅度随涡结构尺寸和流场压缩性而变化; 在涡-涡配对及融合过程中, 涡对中各个涡结构的瞬时对流速度都表现出类似正弦波动的特点. 针对混合层流场中涡结构对流速度的特性, 给出了其背后的物理原因.     

Charged vortex structure in high-temperature superconductors

By using a model Hamiltonian with competing antiferromagnetic (AFM) spin density wave (SDW) and d-wave superconductivity orders, the effect of next-nearest-neighbour (nnn) hopping on spin and charge structures in high-temperature superconductors is investigated at finite temperatures. For an optimally doped sample, we find that the AFM order magnitude in the vortex core is firstly enhanced and then suppressed, accompanied with a ``positively → negatively → positively" charged vortex structure transition with increasing nnn hopping strength, which implies that the AFM order is unnecessarily bounded to an electron-rich vortex core. In addition, a charge ordering pattern with four negatively charged peaks localized in a small region is also found around the vortex core centre without net charge. Recent scanning-tunneling-microscopy experimental observations of the checkerboard structure are hopefully understood.     

入流激励下可压缩剪切层中Kelvin-Helmholtz涡的响应特性

通过直接数值求解Navier-Stokes方程,研究了入流激励下可压缩剪切层中Kelvin-Helmholtz(KH)涡结构的响应特性,结果清晰地展示了KH涡的独特演化方式.基于流动可视化数据,采用两点相关性分析获得了流场拟序结构的空间尺寸和结构角分布.通过分析不同激励频率下涡结构的动态特性,揭示了入流激励下可压缩剪切层中KH涡结构的独特演化机理.研究结果表明,低频入流激励(f=5 k Hz)下KH涡尺寸在远场区域达到饱和后呈现锁频状态,KH涡量厚度稳定在12-14 mm之间;与自由剪切层涡结构通过配对合并的方式实现生长的机理不同,低频入流激励下剪切层的发展是通过中间涡核顺时针吞噬KH不稳定波诱导的一串外围小涡结构来实现生长.此外,针对高频激励(f=20 k Hz)下的剪切层流动,研究了涡结构特性和入流激励参数之间的定量关系,发现均匀分布涡结构的尺寸近似等于对流速度与入流激励频率之比.     

The topological structure of vortex in BEC

We find that there exists an elementary topological current in Bose-Einstein condensation. Based on the -mapping topological current theory, the implicit function theorem and the Taylor expansion, the topological structure of vortex lines is detailed in the neighborhoods of the bifurcation points of the condensate wave function. Received: 9 April 1998 / Revised: 28 August 1998 / Accepted: 31 August 1998     

Interferometry of non-Abelian anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at ν=5/2 and Read-Rezayi state at ν=12/5.     

Smooth non-Abelian bosonization

We present an extension of “smooth bosonization” to the non-Abelian case. We construct an enlarged theory containing both bosonic and fermionic fields which exhibits a local chiral gauge symmetry. A gauge fixing function depending on one real parameter allows us to interpolate smoothly between a purely fermionic and a purely bosonic representation. The procedure is, in the special case of bosonization, complementary to the approach based on duality.     

Aspect on vortex structure in noncentrosymmetric superconductors

Helicity of vortices is studied in a single order parameter Ginzburg-Landau model with n × B term. This unusual term changes the superconductor current, but does not change the quantum of magnetic flux, and the cross helicity of the probability density current in noncentrosymmetric superconductors. In this paper I compute the kinetic helicity and magnetic helicity of a superconductor and introduce a new helicity, i.e. a new topological invariant, to describe vortex phase.     

Interactions of non-Abelian global strings

Non-Abelian global strings are expected to form during the chiral phase transition. They have orientational zero modes in the internal space, associated with the vector-like symmetry SU_(N)L+R$\mathit{SU}{(N)}_{\mathrm{L}+\mathrm{R}}$ broken in the presence of strings. The interaction among two parallel non-Abelian global strings is derived for general relative orientational zero modes, giving a non-Abelian generalization of the Magnus force. It is shown that when the orientations of the strings are the same, the repulsive force reaches the maximum, whereas when the relative orientation becomes the maximum, no force exists between the strings. For the Abelian case we find a finite volume correction to the known result. The marginal instability of the previously known Abelian η^′${\eta }^{\prime }$ strings is discussed.     

Kinetics of vortex structure formation in magnetic materials

A kinetic scenario for the formation of a vortex phase in magnetic materials is discussed. It is found that such a phase can be generated from fluctuations at the kinetic stage of evolution and can subsequently be fixed as a thermodynamically stable phase. Zh. éksp. Teor. Fiz. 111, 1775–1786 (May 1997)     

Multiple off-axis acoustic vortices generated by dual coaxial vortex beams

As a kind of special acoustic field, the helical wavefront of an acoustic vortex(AV) beam is demonstrated to have a pressure zero with phase singularity at the center in the transverse plane. The orbital angular momentum of AVs can be applied to the field of particle manipulation, which attracts more and more attention in acoustic researches. In this paper,by using the simplified circular array of point sources, dual coaxial AV beams are excited by the even-and odd-numbered sources with the topological charges of l_E and l_O based on the phase-coded approach, and the composite acoustic field with an on-axis center-AV and multiple off-axis sub-AVs can be generated by the superimposition of the AV beams for|l_E| ≠ |l_O|. The generation of edge phase dislocation is theoretically derived and numerically analyzed for l_E=-l_O. The numbers and the topological charges as well as the locations of the center-AV and sub-AVs are demonstrated, which are proved to be determined by the topological charges of the coaxial AV beams. The proposed approach breaks through the limit of only one on-axis AV with a single topological charge along the beam axis, and also provides the feasibility of off-axis particle trapping with multiple AVs in object manipulation.     

A nonlinear scenario for development of vortex layer instability in gravity field

A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t ₀ ? t)^?1, where t ₀ is the collapse time.     

Abrikosov vortex core structure in a proximity-effect multilayer

The core structure of the Abrikosov vortex perpendicular to the layers of a proximity effect SN multilayer is discussed. We assume that the superconducting correlations are induced in N via the proximity effect and the dirty limit conditions are fulfilled. The approach for calculation of the local densities of states in N and S layers is developed in the framework of the quasiclassical Usadel equations. For the practically interesting case of SN bilayer, relevant to the STM spectroscopy, the densities of states and apparent STM vortex-core radius, related to the energy-dependent coherence length in N, are calculated.     

The non-Abelian bosonic quantum ring

We investigate the dynamics of a spinor Bose-Einstein condensate which is governed by an optically induced non-Abelian gauge potential. Using a ring shaped trap to confine the atoms and a hydrodynamic ansatz, nonlinear Josephson type equations are found to describe the system. The degenerate eigenstates which show rotation are solved exactly. We consider a homogenous filled ring and observe population dynamics between the two quasi-spin components but also space dependent Josephson oscillations. Stable mass currents can be observed which are induced by the constant non-Abelian effective magnetic field in the limit of weak interactions. For strong interactions the appearance of two-component dark soliton-like objects are observed.     

Entanglement spectrum of non-Abelian anyons

Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.