对偶超导模型n=90—110的近似解析解

研究了对偶超导模型的大n涡旋。 基于变分原理得出了Abelian Higgs模型在n=90—110的近似涡旋解析解, 并计算了涡旋张力对n的依赖性。 发现, 每根涡旋的张力大致随n线性增长。 期望该解对理解Abelian Higgs模型中的大量子数涡旋的墙行为具有一定价值。 The large n vortices in the dual superconductor model was investigated. An approximate analytical solution was obtained for n fold quantized vortices with n=90—110 by variationally solving the AbelianHiggs model, and the vortex tension was calculated as a function of n. It was found that the vortex tension rises linearly as n grows. It is hoped that our solution shines light on the understanding of the wall behavior of the large n vortices in Abelian Higgs model.     

多分量对偶超导理论和口袋模型

基于联络新参数化方案研究了多分量对偶超导模型。给出了多分量Ginzburg Landau模型中的自对偶解, 并研究了磁通量子数趋于无穷大时的墙涡旋解, 以及与口袋模型之间的联系。The multi-component dual superconductor theory has been studied based on the new parameterization of gauge potential. The self dual vortices of the multi component Ginzburg Landau model was investigated. Then we considered the wall vortex whose flux goes to infinity. At last, the relationship between the bag model and wall vortices is considered.     

Three vortex motion in the slightly viscous flow

The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了 Dunne Jackiw Pi Trugenberger 模型中的自对偶方程, 得到一个静态的自对偶Chern Simons多涡旋解, 每个涡旋由5个参数描述。 发现了自对偶解与拓扑数之间的关系, 而拓扑数由Brouwer度与Hopf指标确定。 同时, 也研究了该涡旋解的磁通量的拓扑量子化。The self dual equation and its solution in SU(2) Dunne Jackiw Pi Trugenberger model has Been discussed with special ansatz for the Lie algebraic structures of su(2) and gauge potential decomposition. We obtainer a new concrete self dual equation and found the relationship between SU(2) Chern Simons vortices and topological number which is determined by Hopf indices and Brouwer degrees of  mapping. (two positions, one scale, one phase per vortex and one charge of each vortex) m vortices solutions are discribed by using 5m parameters. The quantization of flux is also studied in this case.     

Multi-types of Skyrmions in SU(N) Quantum Hall System

The skyrmions in SU(N) quantum Hall (QH) system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU( N) QH system there can exist ( N - 1)types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the (N - 1) Cartan subalgebra local bases, we obtain the (N - 1) U(1) electromagnetic field tensors in the SU(N) gauge field of the QH system, and then derive (N - 1) types of skyrmion structures from these U(1) sub-field tensors. Furthermore, in light of the φ-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

Topological Aspects in an Interacting Mixture of a Charged and a Neutral Superfluid in Neutron Stars

By making use of the decomposition of U（1） gauge potential theory and the C-mapping method we discuss a mixture of interacting neutral and charged Bose condensates, which is supposed to be realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonie superconductor. We propose that this system possesses vortex line knotted solitons and the topological charges of vortex lines are characterized by the winding numbers of the C-mapping. Furthermore the spatial bifurcation of vortices is also discussed.     

Multi-types of Skyrmions in SU（N） Quantum Hall System

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.     

Knotted Topological Phase Singularities of Electromagnetic Field

In this paper, knotted objects （RS vortices） in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the Duan＇s topological current theory, we rewrite the topological current form of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum of the linking and self-linking numbers of the knotted RS vortices. Furthermore, the conservation of the Hopf invariant in the splitting, the mergence and the intersection processes of knotted RS vortices is also discussed.     

Topological aspect of Chern--Simons p-branes

By generalizing the topological current of Abelian Chern--Simons (CS) vortices, we present a topological tensor current of CS p-branes based on the \phi -mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field \phi(x), and the topological structure of CS p-branes is characterized by the winding number of the \phi-mappings. Furthermore, the Nambu--Goto action and the equation of motion for multi CS p-branes are obtained.     

双层量子霍尔系统在填充因子υ=1/2态的涡流解(英文)

以双层系统的ZHK 模型为基础,研究了双层量子霍尔系统在朗道填充因子取υ = 1=2 这种状态的静态涡流解。ZHK模型是一种包含Chern-Simons 规范相互作用的有效理论。为了简便,假定涡流具有柱对称的结构,随后写出了无量纲的非线性运动方程组,并分析了解的渐进行为。另外,在自对偶条件下,确定了自耦合常数的形式,并写出了关于密度的自对偶方程。最后,使用数值方法找到了类型分别为(0,1),(0, -1),(1,-1) 和(-1,-1) 的涡流解。发现拓扑数为(1,-1) 的涡流是不稳定的,它会衰变为(1,0) 和(0,-1) 两种涡流。数值结果表明,拓扑数为(0,-1)和(-1,-1)的涡流确实是自对偶涡流解。We investigate the static vortex solutions of a bilayer quantum Hall state at the Landau-level filling factor υ = 1=2. This work is based on the ZHK model, which is an effective field theory including Chern-Simons gauge interactions. We deduce the dimensionless nonlinear equations of motion for vortices possessing cylindrically symmetry, and analyze the asymptotical behaviors of solutions. Additionally, we analyze the values of critical coupling constants under the self-dual condition, and obtain the self-dual equations. Finally, vortices of type (0,1),(0, -1),(1,-1) and (-1,-1) are solved with numerical methods. We reach the conclusion that vortex of type (11,-1) is unstable, which will decay to (1,0) and (0,-1). The vortices of type (0,-1) and (-1,-1) are self-dual solutions from numerical results.     

Self-dual Chern–Simons Vortices on Bounded Domains

In this Letter we consider the Abelian Chern–Simons vortices on a bounded simply connected domain. We establish the existence of solutions for the self-duality equations. We prove the uniqueness of solutions when all the vortex points are equal and the domain is star-shaped. We also show the radial symmetry of solutions on balls centered at the vortex point.     

Effective monopole potential for SU(2) lattice gluodynamics in the spatial maximal Abelian gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the spatial maximal Abelian gauge. This gauge is more physical than the ordinary maximal Abelian gauge due to absence of nonlocalities in the temporal direction. We show numerically that in the spatial maximal Abelian gauge the probability distribution of the Abelian monopole field is consistent with the dual superconductor mechanism of confinement: the Abelian condensate vanishes in the deconfinement phase and is nonzero in the confinement phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 166–170 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Interaction between optical phonons and Josephson vortices in layered superconductors

The effect of optical phonons on the stability of the in-phase motion regime of Josephson vortices in a layered superconductor has been studied by using an expression for the dielectric constant of a layered high-temperature superconductor. The dispersion characteristics of linear waves have been analyzed. It has been shown that the in-phase motion regime of the Josephson vortices can be spontaneously established in the layered superconductor.     

Topological vortices in a two-gap superconductor

Based on the ϕ-mapping theory, we derive a new rigorous equation describing the distribution of the magnetic field for vortices in a two-gap superconductor, of which the so-called modified London equation is just a special case in a one-flavor limit. We explicitly investigate the London penetration depth, the Meissner and mixed states and Josephson effect. A magnetic flux quantization condition for vortices in a two-gap superconductor is also derived, from which it follows that in a two-gap superconductor there exist vortices which carry an arbitrary fraction of magnetic flux quantum. The branch processes during the evolution of the vortices in a two-gap superconductor are discussed.     

Non-Abelian statistics of half-quantum vortices in p-wave superconductors

Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core we derive the non-Abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.     

Lattice vortices in the two-dimensional Abelian Higgs model

We generate and identify multi-vortices of the 2D Abelian Higgs model on a finite lattice by relaxation of Monte Carlo equilibrium configurations. The lattice vortices have action and a uniquely defined topological charge corresponding to the continuum ones. They exhibit the expected exponential decay behaviour and satisfy approximately the classical equations of motion. Vortex-antivortex superpositions are seen as well, supporting the dilute gas picture. Single vortices finally relax into “dislocations” and disappear. A background charge construction turns out nearly insensitive with respect to dislocations.     

Instanton solutions from Abelian sinh-Gordon and Tzitzeica vortices

We study the Abelian Higgs vortex solutions to the sinh-Gordon equation and the elliptic Tzitzeica equation. Starting from these particular vortices, we construct solutions to the Taubes equation with higher vortex number, on surfaces with conical singularities.We then, analyse more general properties of vortices on such singular surfaces and propose a method to obtain vortices on conifolds from vortices on surfaces of revolution. We apply our method to construct explicit vortex solutions on the Poincaré disk with a conical singularity in the centre, to which we refer as the “hyperbolic cone”.We uplift the Abelian sinh-Gordon and Tzitzeica vortex solutions to four dimensions and construct cylindrically symmetric, self-dual Yang–Mills instantons on a non-self-dual (nor anti-self-dual) 4-dimensional Kähler manifold with non-vanishing scalar curvature. The instantons we construct in this way cannot be obtained via a twistorial approach.