Soliton pair creation at finite temperatures: Numerical study in (1 + 1) dimensions

Creation of soliton-antisoliton pairs at finite temperature is considered within a (1 + 1)-dimensional model of a real scalar field. It is argued that at certain temperatures, the soliton pair creation in quantum theory can be investigated by studying classical field evolution in real time. The classical field equations are solved numerically, and the pair creation rate and average number of solitons are evaluated. No peculiar suppression of the rate is observed. Some results on the sphaleron transitions in (1 + 1)-dimensional abelian Higgs model are also presented.     

Quantum S-matrix of the (1 + 1)-dimensional Todd chain

Exact factorized S-matrices are proposed for two models of (1 + 1)-dimensional quantum field theory: the Z(N) symmetric (1 + 1)-dimensional Todd chain and the e^? + e^?2? model.     

Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity

In the context of the formalism proposed by Stelle-West and Grignani-Nardelli, it is shown that Chern-Simons supergravity can be consistently obtained as a dimensional reduction of (3 + 1)-dimensional supergravity, when written as a gauge theory of the Poincaré group. The dimensional reductions are consistent with the gauge symmetries, mapping (3 + 1)-dimensional Poincaré supergroup gauge transformations onto (2 + 1)-dimensional Poincaré supergroup ones.     

2+1维刻蚀模型生长表面等高线的共形不变性研究

为了更全面、有效地研究刻蚀模型(etching model)涨落表面的统计性质,基于Schramm Loewner Evolution(SLEκ)理论,对2+1维刻蚀模型饱和表面的等高线进行了数值模拟分析.研究表明,2+1维刻蚀模型饱和表面的等高线是共形不变曲线,可用Schramm Loewner Evolution理论进行描述,且扩散系数κ=2.70±0.04,属κ=8/3普适类.相应的等高线分形维数为df=1.34±0.01.     

A SOLVABLE 1+1-DIMENSIONAL U(1) GAUGE THEORY

A 1+1-dimensional U(1+1) gauge theory is proposed and the exact solution of its spectrum and corresponding energy eigenstates is found.     

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.     

二维电子体系在高密度下的稳定性

本文计算了高密度的二维电子体系的边缘能(将二维体系沿某一直线解离成两片时,形成单位长度新边缘所需要的能量)。结果发现,当r_ss^(c)(约0.415)时,边缘能变负,从而表明在高密度下,二维电子气的基态有可能发生不稳。我们分别讨论了二维非束缚的电子气和束缚的电子气基态的稳定性,并在一个简化的模型下给出了束缚的电子气基态稳定性的判据。 关键词：     

An (n+1)-Dimensional Integrable Model: Painlevé Test

A (3+1)-dimensional model is proposed at first. The integrability of the model is proved by using the standard Painlevk analysis. Then the model is extended to (n + 1)-dimensional case. The model is space-isotropic and is a type of the modified KdV extension in higher dimensions.     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.     

A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.     

1+1维Wolf-Villain模型生长表面高度极值统计分布的数值模拟

为全面研究Wolf-Villain(WV)模型生长表面的统计性质,基于极值统计理论,模拟计算1+1维WV模型在饱和生长阶段表面的极大高度分布(maximal-height distribution,MAHD)和极小高度分布(minimal-height distribution,MIHD).结果表明,MAHD和MIHD在不同的系统尺寸下分别有较好的标度规律,这两个分布之间存在不对称性.其中,MAHD遵循-种常见的极值分布,即广义的Fisher-Tippett-Gumbel(FTG)型分布;而MIHD可以用-个修正的Fisher-Tippett-Gumbel(MFTG)型分布来描述.     

湍流边界层内流向涡的数值模拟研究

采用准二维共振三波作为湍流边界层近壁区相干结构初值,用直接数值模拟方法计算了流动从二维结构发展到三维结构并且伴随流向涡生成的整个过程,分析结果显示流向涡对湍流动能和质量传输有着重要作用,是湍流边界层相干结构的重要特征和运动形式.     

THE CRITERION FOR FRACTIONAL CHARGE OF(1+1)-DIMENSIONAL DIRAC FIELD

The fractional fermion number (charge) of (1+1)-dimensional Dirac field interacting with a scalar background field is investigated. By means of the correspondence principle in (1+1)-dimensional field theory,it is shown that only when the background field develops a solitvn with a node can the fractional fermion number be induced(node theorem).Consistently, a zero mode bound state of the fermion field should be present and responsible for the fractional charge as long as the soliton satisfies certain conditions (theorem of zero mode).We have also obtained the analytical expression of the vacuum charge distribution in the vicinitu of distorted reqion.     

Creation of a time-machine in (2+1)-dimensional gravity

A non-stationary model of two concentric counter-rotating layers is constructed in (2+1)-dimensional Einstein theory. It is shown that the model which satisfies both the weak and the dominant energy conditions, may evolve from a state with no closed time-like curves to a state where such curves are present in a finite region of space. No singularities are formed in the process.     

Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D spacetime variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.      

Geometrical meaning of braid statistics in (1+1)- and (2+1)-dimensional quantum field theory

Braids naturally arise as topological objects in the discussion of statistics in quantum mechanics of indistinguishable pointlike particles moving in a (2+1)-dimensional space-time. Conversely, they also play a role as algebraic invariants in the discussion of superselection rules in (1+1)-dimensional algebraic quantum field theory. Here we show how Abelian braid statistics in (1+1) dimensions may be interpreted geometrically by introducing the concept of antiparticles, thus clarifying the connection between the two approaches.     

Interactions Between Solitons and Cnoidal Periodic Waves of the (2+1)-Dimensional Konopelchenko-Dubrovsky Equation

The (2+1)-dimensional Konopelchenko-Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the (2+1)-dimensional Konopelchenko-Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is solved by the consistent Riccati expansion (CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the (2+1)-dimensional Konopelchenko-Dubrovsky equation.     

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

We demonstrate a few striking similarities and some glaring differences between (i) the free four- (3+1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two- (1+1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. With the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge-invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.     

一个4+1维宇宙模型

我们讨论的4+1维宇宙模型是通常的四维时空和一个紧致的一维内禀空间的直积空间。我们假定四维时空的能量密度是以辐射为主的,而内禀子空间的能动张量是一个阶跃函数。通过求解五维的Einstein场方程得到前四维时空由de-Sitter解过渡到标准模型的辐射为主解,与此同时内禀子空间的尺度由减幅振荡过渡到为按t的负幂次收缩而趋于一常量。 关键词：     

(1+1)维耦合Ito系统的单值和多值局域激发模式

在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等.