EFFECTS OF THE SOLITON CONFIGURATION ON THE LOCALIZED MODES IN POLYACETYLENE

The exact static configuration of the soliton in polyacetylene is determined through the self-consistent iterations and the localized modes around the soliton are numerically caiculated. They are compared with the results that the static configuration of the soliton is assumed to be the kink u₀tanh(n/L). The comparison shows that the self-consistent configuration improves the Goldstone mode by getting the positive-definite vibrational matrix, whereas the other localized modes change their frequencies only less than 0.03%. It confirms that the five localized modes around the soliton do exist in polyacetylene.     

Neutral solitons in polyacetylene: Implications of the ENDOR results

We demonstrate that the ENDOR results on polyacetylene are consistent with the soliton model, and that ENDOR data measure the size of the chain segment over which a soliton diffuses. The existence of two discrete sites is a confirmation of the qualitative feature of the soliton gap state wave-function which has amplitude only on alternate sites. The observation of negative spin density (rather than zero) on the second kind of site requires that the model be expanded to include the electron-electron Coulomb interaction which leads to the observed negative exchange polarization.     

Spin-lattice relaxation by solitons in 13C enriched iodine doped trans-poly acetylene

An experimental study of NMR spin-lattice relaxation of ¹³C in enriched, iodine doped, polyacetylene is presented together with a theoretical analysis of the results based on the existence of solitons in this system. The good agreement with this model and the numerical values obtained here and those measured by different experimental techniques support firmly the applicability of the soliton picture to I₂ doped polyacetylene.     

Lattice soliton equation hierarchy and associated properties

As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.     

电子关联和孤子

聚乙炔中的电子关联和孤子可用相关基函数方法(CBF)来研究,通过考虑完全的电子-电子相互作用,得到含有单个电荷的奇数原子链的稳定位形为孤子的结论,随着电子-电子互作用强度U和互作用程α/β的增加,孤子定域性加强,产生能降低,因此,即使计入电子-电子相互作用,孤子仍然是导电聚合物中的主要载流子。 关键词：     

Soliton and kink jams in traffic flow with open boundaries

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.     

Chain length dependence of localized vibrational modes around a soliton in trans-polyacetylene

Vibrational frequencies of finite polyacetylene with a charged soliton are calculated using the molecular orbital method. It is found that the frequency of the translational mode has a remarkable length effect and is inversely proportional to the square of chain length. The dependence is explained by regarding the soliton as a quantum particle in a one dimensional box.     

Dynamics of self-localized excitations in a polyacene chain

Dynamical formation processes of self-localized excitations induced by charge injection or photoexcitations in a polyacene chain are investigated by a nonadiabatic dynamic method. The polyacene chain is treated as two alternatively coupled polyacetylene chains. The initial lattice configuration is taken as the pristine polyacene chain. It contains an interchain-coupled neutral soliton as a consequence of odd-number sites in each of the two chains. The nonadiabatic dynamical processes are carefully investigated in the following physical cases: (1) electron injection; (2) electron transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO); (3) electron transition from HOMO to the localized soliton level, and (4) electron-hole pair excited at the continuum absorbtion edge for light polarized parallel to the chain. It is interestingly found that the centers of the electron and the hole excited by light polarized parallel to the chain are separated. Therefore, the photogenerated charge carriers should be favorable in polyacene, which is remarkably different from those found in a single polyacetylene chain.     

Amplitude recurrence of the staggered mode in nonlinear diatomic macro-lattice

The staggered soliton mode, which was first discovered in polyacetylene, was observed by Lou et al. in a one-dimensional nonlinear pendulum-lattice. Some recurrence phenomena of the amplitude of the staggered mode in a macro-lattice system are investigated. The experimental result shows that the amplitude of the envelope soliton changes periodically or quasiperiodically under suitable excited parameters. In addition, a period doubling bifurcation is also observed.     

Quantum fluctuations of spatial dissipative solitons in a nonlinear interferometer

A quantum Langevin equation is derived that makes it possible to study the radiation field in a large-aperture nonlinear interferometer excited by external classical radiation. This equation is linearized in the vicinity of the solution for a stationary soliton. A mathematical formalism for obtaining a spectral representation of the solution to the linearized problem is constructed. It is shown that, in general, the excitation spectrum of a soliton consists of three branches, two of which belong to a continuous spectrum, while the third branch is discrete. The spectral representation obtained makes it possible to rigorously define the operator of soliton coordinate fluctuations, since, as is shown in the study, the traditional definition of this operator leads to a divergence in the vicinity of the solution. A new type of dissipative soliton is found, which is a natural generalization of a stationary soliton and takes into account its motion. A relation is found between this soliton and the contribution to the solution for field fluctuations from the discrete spectrum expansion. The mean squares of fluctuations of the soliton coordinate and momentum are calculated. A range of parameters is determined where the momentum of the soliton can always be measured with a spread smaller than the standard quantum limit. This possibility is related to the occurrence of states squeezed with respect to the soliton momentum. A scheme is proposed for the experimental observation of these states.     

Solitons in superlattices: A tight-binding approach

We present a tight-binding approach of the soliton formations and propagations in superlattices. Negative differential conductivity in superlattices leads to the growth of the inevitable spatial fluctuations and formation of the electron accumulation-layer domain. Based on the negative differential conductivity, it is shown that the envelope of the tight-binding-approach wave functions is governed by the nonlinear Schrödinger equation which has soliton solutions, the result of which suggests soliton formations and propagations in the superlattices.     

Solid-state lithium/polyacetylene battery

A solid-state lithium/iodine battery has been formed by directly contacting metallic lithium with iondine-doped polyacetylene. The procedure is similar to that used for the well-known lithium/iodine-polyvinylpyridine system. The advantage of the system proposed here may be related to the extraordinary electrical properties of polyacetylene which, when doped with iodine, acquires a very high electrical conductivity over a wide range of halogen concentration.     

碘掺杂聚乙炔电子自旋共振及导电性的研究

用四探针法测量掺碘聚乙炔薄膜[CH(I₃)_y]_x,当y=1.0％,4.2％和8.3％时面电阻随温度的变化,发现它们可用变程跳跃(VRH)模型很好的描述。用电子自旋共振(ESR)谱仪研究了不同温度下低浓度碘掺杂聚乙炔的自旋磁化率、峰峰宽等。并给出相应的理论解释。 关键词：     

Soliton analysis of the electro-optical response of blue bronze

In recent measurements on the charge-density-wave (CDW) conductor blue bronze (K_0.3MoO₃), the electro-transmittance and electro-reflectance spectra were searched for intragap states that could be associated with solitons created by injection of electrons into the CDW at the current contacts [Eur. Phys. J. B16 (2000), 295; Eur. Phys. J. B35 (2003) 233]. In this work, we adapt the model of soliton absorption in dimerized polyacetylene to the blue bronze results, to obtain the (order of magnitude) estimate that current induced solitons occur on less than ∼10% of the conducting chains. We discuss the implications of these results on models of soliton lifetimes and motion of CDW phase dislocations.     

Interaction Between Line Soliton and Algebraic Soliton for Asymmetric Nizhnik-Novikov-Veselov Equation

Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.     

Asymptotic theory of plane soliton self-focusing in two-dimensional wave media

An asymptotic method is developed to describe a long-term evolution of unstable quasi-plane solitary waves in the Kadomtsev-Petviashvili model for two-dimensional wave media with positive dispersion. An approximate equation is derived for the parameters of soliton transversal modulation and a general solution of this equation is found in an explicit form. It is shown that the development of periodic soliton modulation, in an unstable region, leads to saturation and formation of a two-dimensional stationary wave. This process is accompanied by the radiation of a small-amplitude plane soliton. In a stable region, an amplitude of the modulation is permanently decreasing due to radiation of quasi-harmonic wave packets. The multiperiodic regime of plane soliton self-focusing is also investigated.     

Doping induced disorder in trans-polyacetylene: A spectroscopic and dynamical study

The results of lattice dynamical calculations on pristine and doped trans- polyacetylene are summarized and a reinterpretation of the vibrational spectrum is suggested. The possibility of the existence in the doped system of a centrosymmetrical molecular defect, consistent with the infrared spectrum, alternative to the soliton defect is discussed.     

Explicit N-Solit on Solution of the Unstable Nonlinear Schrödinger Equation

The unstable nonlinear Schrodinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov-Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated.     

Painlevé analysis and exact solutions of the resonant Davey-Stewartson system

It is shown that the resonant Davey-Stewartson (RDS) system can pass the Painlev test. By truncating the Laurent series to a constant level term, a dependent variable transformation is naturally derived, which leads to the bilinear forms of the RDS system. From the bilinear equations, through making suitable assumptions, some new soliton solutions are obtained. Some representative profiles of the solitary waves are graphically displayed including the two-line soliton solution, “Y” soliton solution, “V” soliton solution, solitoff, etc. The solutions might be useful to describe the nonlinear phenomena in Madelung fluids, capillarity fluids, and so on.     

1:3 Peierls系统中的极化子

在可约数为3的一维Peierls系统中,我们运用SSH模型的连续极限得到了极化子解。在弱耦合极限下,这一极化子解严格满足离子位移序参量的自洽条件。我们给出了极化子的形成能和特征宽度,并讨论了可约数为M的一般情况下可能的孤子激发。 关键词：