Bosonization,topological solitons and fractional charges in two-dimensional quantum field theory

We further develop the quantization of topological solitons in two-dimensional quantum field theory in terms of Euclidean region functional integrals. Our approach is nonperturbative and mathematically rigorous. We apply it to construct physical states with fractional fermion number in models of interacting bosons and fermions without recurring to a semiclassical approximation. A related issue discussed in this paper is two-dimensional chiral bosonization.     

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.     

Dynamic topological solitons in a two-dimensional ferromagnet

It is shown that stable, skyrmion-type, dynamic solitons can be constructed for a wide class of two-dimensional models of anisotropic ferromagnets. These solitons are stabilized as a result of the conservation of various integrals of motion: the z projection of the total spin S _z or the orbital angular momentum L _z of the magnetization field. A class of two-parameter solitons with quite complicated (almost periodic) magnetization-field dynamics exists for a purely uniaxial model (in the sense of both spin and spatial rotations) with maximum symmetry. Stable solitons with periodic magnetization dynamics exist for ferromagnets with lower symmetry (only S _z or L _z or the total angular momentum J _z =L _z +S _z is conserved). Zh. éksp. Teor. Fiz. 115, 1511–1530 (April 1999)     

Dynamics of topological solitons in two-dimensional ferromagnets

Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations.     

带有相反拓扑指数的光学涡流间相互作用研究

对线性介质中光学涡流间相互作用做了数值分析，发现当拓扑指数相反时，含有涡流对的光场产生了类似于对称破缺的不稳定性，螺旋位错在传播过程中演变为一种新的位错——边位错，作用过程中拓扑指数守恒. 关键词： 光学涡流 拓扑指数 位错     

Dynamical correlation from topological solitons in two-dimensional anisotropic models

The structure and dynamics of soliton configurations are considered for a two-dimensional classical Heisenberg model in the XY-and Ising-like models. Using a phenomenology based on a dilute gas of mobile solitons we obtain a central peak (=0) for dynamical correlation functions.     

On stationary topological solitons in a two-dimensional anisotropic Heisenberg model

We study stationary two-dimensional solitons in an easy-axis Heisenberg magnet with the Hamiltonian density wherei=1, 2,a=1, 2, 3, and (x _i ) is the angle between unit vector s(x _i ) and the easy axis, 0<p<. Stable solitons with a topological chargeQ=1 and localized distributionss ^a (x _i ) withQ=2 are found. The existence of the bound states of two solitons withQ=1 is shown numerically for 0<p<.     

相反拓扑指数的Laguerre-Gaussian模的产生和模间相互作用的实验研究

实验研究了带有相反拓扑指数的Laguerre-Gaussian(LG)模间的相互作用，发现含有相反拓扑指数的两个LG模在传播过程中其光场发生变化，观察到随着传播距离的增加，两个LG模的中心位相奇点会逐渐连成为一个弧形暗线形状.实验上验证了带有相反拓扑指数的光学涡流中的螺旋位错在传播过程中会演变为边位错这一理论结果.     

Multicomponent dipole-mode spatial solitons

We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.     

On topological excitations with isovector topological charges

It is shown that degenerate systems with order parameter ψ taking on values in compact homogeneous subspaces T _G or G/T _G (where G is a simple compact group and T _G is its maximum commutative subgroup) possess a rich collection of topological excitations (vortices or, correspondingly, instantons) with isovector topological charges. The corresponding homotopy groups are found for all G. The possibility of a topological interpretation of the quantum numbers of the groups and particles is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 758–762 (25 May 1996)     

Stabilized two-dimensional vector solitons

In this Letter, we introduce the concept of stabilized vector solitons as nonlinear waves constructed by the addition of mutually incoherent fractions of Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of these new kinds of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.     

Multicomponent gap solitons in superposed grating structures

We demonstrate, numerically, the existence and stability of multicomponent gap solitons in a Kerr nonlinear medium with a superposed grating based on a derived system of coupled-mode equations. Applications to all-optical logic and signal processing are discussed.     

Supersymmetry algebras that include topological charges

We show that in supersymmetric theories with solitons, the usual supersymmetry algebra is not valid; the algebra is modified to include the topological quantum numbers as central charges. Using the corrected algebra, we are able to show that in certain four dimensional gauge theories, there are no quantum corrections to the classical mass spectrum. These are theories for which Bogomolny has derived a classical bound; the argument involves showing that Bogomolny's bound is valid quantum mechanically and that it is saturated.     

Partition function for two-dimensional solitons

The partition function for two-dimensional scalar field theories which possess soliton states, is constructed in the semi-classical approximation. Divergences are handled by using zeta-function methods. The result is naturally interpretated after the appropriate mass renormalisations, as being that due to a massive particle confined in a box.     

Observation of two-dimensional surface solitons

We report the first experimental observation of two-dimensional surface solitons at the boundaries (edges or corners) of a finite optically induced photonic lattice. Both in-phase and gap nonlinear surface self-trapped states were observed under single-site excitation conditions. Our experimental results are in good agreement with theoretical predictions.     

Large-radius dynamic topological solitons in uniaxial ferromagnets

In thin ferromagnetic films with perpendicular anisotropy, there exist stable large-radius dynamic topological solitons, which are stabilized owing to conservation of the orbital angular momentum of the magnetization field. The solitons can also exist if the projection of the total spin moment of the magnet onto the easy axis is not conserved, i.e., in the absence of pure uniaxial symmetry of the model. Even in the pure uniaxial case, the magnetization distribution in a soliton with a sufficiently large radius differs significantly from centrosymmetric.     

Observation of two-dimensional multimode solitons

We present the first experimental observation of (2+1) -dimensional multimode (composite) solitons. A single-hump component and a double-hump (dipole-type) component are jointly self-trapped as a composite soliton in a biased photorefractive crystal.     

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.