<Emphasis Type="Italic">Q</Emphasis> kink of the nonlinear <Emphasis Type="Italic">O</Emphasis>(3) <Emphasis Type="Italic">σ</Emphasis> model involving an explicitly broken symmetry

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S ¹, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [−1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.     

Internal mode dynamics in driven nonlinear Klein-Gordon systems

We study analytically and numerically the action of a constant force on the propagation of kinks in the φ⁴ and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution. Finally, we show that for the φ⁴ system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical simulations. Received 6 June 2000     

On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin–Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number. Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001     

Oscillating Propagation of Kink in Nondissipative Frenkel-Kontorova Chain Due to External DC Force

We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink ＆ transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.     

Kink dynamics in the highly discrete sine-Gordon system

We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case: they lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states, while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations. When a small external driving force is applied to the system, the same velocities appear as plateus in the strongly nonlinear mobility of the kink. The energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system, and the preferential velocities for the kink are obtained to good accuracy. Similar results may be expected to be valid for other discrete systems manifesting topological solitons. The numerical simulations reveal also new stable “multiple-kink” excitations which can propagate almost freely in extremely discrete systems where “ordinary” simple kinks are pinned to the lattice by discreteness. The stability of the “multiple-kinks” is discussed.     

Comment on relativistic ideal soliton-gas approximations

We comment on the validity of using relativistic, ideal, Boltzmann-kink-gas phenomenology involving “bare” kinks for interpretation of experiments and molecular dynamics simulations. An improved velocity distribution is obtained for sine-Gordon and ?-four kink gases which incorporates the kink renormalization found to be essential in obtaining the correct total kink density. We argue, however, that even with this improvement, current ideal gas phenomenologies can only be trusted at low temperatures compared to the kink rest energy, where the majority of kinks have low velocity in any case.     

扭结孤子牛顿动力学行为的奇异摄动理论

利用奇异摄动展开,发展了一种研究sine-Gordon扭结孤子动力学行为的理论,得到了在恒定外力作用下sine-Gordon扭结孤子类似于经典粒子,其运动遵守牛顿运动定律.同时,还得到了它在传播过程中所辐射的色散波的一个形式简单的解析表达式. 关键词： 扭结孤子 奇异摄动展开 动力学行为     

Propagation and stability of kinks in driven and damped nonlinear klein-gordon chains1

We consider the propagation of kinks in an elastic chain in a bistable or multistable potential under the action of a driving force [M. Büttiker and H. Thomas,Phys. Rev. A 37:235 (1988)]. Each element of the chain is subject to a damping force proportional to its velocity. We show that both the propagation velocity of the kinks as a function of the driving field, and the kink width as a function of propagation velocity, are determined by characteristic functions which depend only on the form of the potential. These functions can be found by considering a single particle moving in the upside-down potential of the chain. The general properties of these functions are studied and illustrated by several examples. The stability of these driven kinks is discussed. Interestingly, we find in addition to the expected discrete localized eigenmodes a two-dimensional continuum of oscillatory modes with a localized envelope.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Neutral bound states in kink-like theories

In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay. A phase space estimate of these decay rates is also given. This shows that there may be a window of values of the coupling constant where a particle with higher mass is more stable than the one with lower mass. We also discuss the crossing symmetry properties of the semiclassical form factors and the possibility of extracting the elastic part of the kink S-matrix below their inelastic threshold. We present the analysis of theories with symmetric and asymmetric wells, as well as of those with symmetric or asymmetric kinks. Illustrative examples of such theories are provided, among others, by the tricritical Ising model, the double sine-Gordon model and by a class of potentials recently introduced by Bazeia et al.     

Haldane Gap in One-Dimensional Spin Chains

One-dimensional antiferromagnetic spin chains (S = 1) are quantized by means of the Gaus sian effective potential method for the O(3) nonlinear a model. The critical line-separating the missive phase with Haldane gap and massless phase is found in an analytic form. The spin correlation function is discussed via the sine-Gordon formulation as well.     

Ginzburg–Landau theory of multi-band superconductivity and applications to Fe pnictides

We investigate multi-component superconductors, in relation to iron pnictides, by using the Ginzburg–Landau theory. We show that a three-band superconductor exhibits several significant properties that are not found in single-band or two-band superconductors. The frustrating pairing interaction among Fermi surfaces may lead to a time-reversal symmetry broken pairing state. In fact, we have a solution with time-reversal symmetry breaking, that is, a chiral solution when there is such a frustration. The Ginzburg–Landau equation for three-component superconductors leads to a double sine-Gordon equation. A kink solution exists to this equation that results in the existence of fractional-quantum flux vortices on the domain wall.     

Force-extension curve of a polymer in a high-frequency electric field

We study theoretically the conformation and force-extension curve of a semiflexible polymer in a spatially uniform ac electric field. The polymer backbone minimizes its energy by aligning along one of two orientations parallel to the field. In a strong ac field, hairpin kinks develop between regions of opposite alignment. These kinks are mathematically described as sine-Gordon solitons. We calculate the equation of state of the one-dimensional kink gas, which yields the force-extension curve of the polymer. A sufficiently strong ac field causes the polymer to extend spontaneously to almost its full contour length. The theory is applied to recent experiments on dielectrophoretic stretching of DNA.     

Kinematics of the forced and overdamped sine-Gordon soliton gas

Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation and subsequent annihilation of pairs of kinks and antikinks. We show that in the steady state there are no spatial correlations between kinks or between kinks and antikinks. For a given number of kinks and antikinks all geometrical distributions are equally alike, as in equilibrium. A master equation for the probability distribution for the number of kinks on a finite chain is solved, and substantiates the physical reasoning in previous work. The probability distribution characterizing the spread along the direction of particle motion of a finite chain in equilibrium as well as in the driven overdamped case is derived by simple combinatorial considerations. The spatial spread of a driven chain in the thermodynamic limit does not approach a steady state; a given particle followed in time deviates as t^1/2 from its average forced motion. This result follows from the hydrodynamic equations for the dilute kink gas. Comparison is made with other recent results.     

A Special Two-Soliton Solution of sine-Gordon Equation

A special two-soliton solution of sine-Gordon equation is obtained by using the Hirota direct method. It is shown in a mass-centre system how two kinks move and interact with each other.     

Exact and numerical solutions to the perturbed sine-Gordon equation

We present numerical and analytic solutions to the perturbed sine-Gordon equation, which models long Josephson tunnel junctions. We make comparisons between numerical results and results obtained from perturbational methods. We present unstable, analytic kink solutions to the equation and further a solution, which is an array of kinks, corresponding to a solution, where the current through the junction is larger than the critical current.     

Properties of IR-active lattice vibrations in the vicinity of kinks in the Frenkel-Kontorova model

The properties of infrared lattice vibrations in the presence of kinks in the Frenkel-Kontorova model are analyzed. Our results show that the vibration of particles involved in kink formation is very similar to that in a gap mode around a force-constant defect. We found that the IR phonon mode intensity possesses a universal dependence on a certain combination of system parameters and kink concentration. On the basis of these results a criterion is proposed for separating the regime of weakly interacting kinks in the system from the regime of a kink lattice. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 750–754 (25 May 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fermi-Dirac Kink Propagation in High-Order Nonlinear Media

We show analytically that addition of a quintic term to the positive Kerr-type nonlinearity offers a unique type of kink soliton-like solution with Fermi-Dirac profile. This type of optical kink allows, in contrast to other optical kinks discovered so far, stationary kink formation not only in the time domain but in the spatial domain. The latter could admit of a route for the first time to our knowledge to spatial kink solitons of intensified laser beams. The underlying principle of the optical kink propagation is described.     

多间隙耦合腔电子电导与模式稳定性

根据空间电荷波小信号基础理论,建立了多间隙耦合腔中单个间隙电子电导的计算模型与模式稳定性分析模型。以3间隙耦合腔为例,推导出了各个间隙电子电导的计算公式。通过理论计算与仿真模拟,研究了3间隙耦合腔中各个模式的电子电导特性,并进行了间隙中注波互作用研究与模式稳定性分析。模型计算发现:各个间隙不同模式的电子电导不同,第3间隙内电子电导受注电压及间隙距离影响最大,对整个间隙内的注波互作用及电路稳定性的影响也最大。该模型还可以用于分布作用速调管注波互作用的计算模拟。     

The quantum kinks of two-dimensional theories of the φ4 type

We apply a recently established method of kink quantization, to two-dimensional theories of the φ⁴ type possessing either a Z(4) × O(N) or an SU(N) symmetry and containing N complex scalar fields. Correlation functions of kinks are estimated through a 1/N expansion. Quantum kinks are interpolated by a local field, whenever a broken symmetry phase occurs. These kinks are massless. This result holds up to all orders in 1/N.