电子关联对顺式聚乙炔中双极化子附近局域振动模的影响

用自洽迭代的方法研究了顺式聚乙炔中双极化子的能谱及其附近的局域振动模.结果发现:1)在顺式聚乙炔中,双极化子的电子束缚态数目和位置仅取决于耦台参数λ和电子相互作用U,这类似于反式聚乙炔;参数t_l(消除基态二度简并)虽不能改变电子局域态的个数,但影响了双极化子附近局域模的数目.2)电子相互作用不仅使局域模的频率发生了漂移,而且增加了局域模的个数,这不同于反式,3)局域模的局域性随耦合参数λ以及电子相互作用U的增加而增强,随参数(?)的增大而减弱.     

电子关联对顺式聚乙烯中双极化子附近局域振动模的影响

用自洽迭代的方法研究了顺式聚乙炔中双极化子的能谱及其附近的局域振动模。结果发现：１）在顺式聚乙炔中，双极化子的电子束缚态数目和位置仅取决于耦合参数λ和电子相互作用Ｕ，这类似于反式聚乙炔；参数ｔ１（消除基态二度简并）虽不能改变电子局域态的个数，但影响了双极化子附近局域模的数目。２）电子相互作用不仅使局域模的频率发生了漂移，而且增加了局域模的个数，这不同于反式。３）局域模的局域性随耦合参数λ以及电子相     

Na掺杂反式聚乙炔中的孤子晶格的能谱与电子束缚态

从离散的ＳＳＨ模型出发，考虑了链内的电子相互作用，以及由杂质和周围链上的荷电孤子产生的库仑势的影响，探讨了各种掺杂浓度的反式聚乙炔中孤子晶格的能谱与电子束缚态。计算结果表明：在孤子晶格的能谱中，在价带底有两条定域能级，在导带顶存在着多个电子束缚态，随掺杂浓度的升高，束缚态的局域性减弱，禁带中的孤子能级形成孤子能带。当掺杂浓度高达１６．６７％时，所有的电子束缚态都消失，转变为扩展态。孤子晶格的禁带宽度随着掺杂浓度的增加而增大，最高占据态与导带底之间的能隙则随之逐渐减小。孤子能带底与价带顶之间的能隙在临界浓度附近有一极大值。还讨论了电子－电子相互作用对孤子晶格能谱的影响。 关键词：     

聚噻吩中双电子极化子附近的二维局域振动模

将聚噻吩的一维SSH孤子模型推广到二维平面,研究了聚噻吩双电子极化子附近的二维局域振动模.计算结果表明双电子极化子附近存在15个局域振动模,其中4个奇宇称模与4条强红外吸收谱线1020,1120,1200,1323cm^-1相对应,4个偶宇称模恰与4条Raman吸收峰700,1047,1175,1220cm^-1一致. 关键词：     

链间耦合对反式聚乙炔中孤子能谱及其局域振动模的影响

从计及了链间相互作用项的ＳＳＨ模型出发，讨论了相邻两条链间电子跃迁对反式聚乙炔中孤子能谱及孤子附近的局域振动模的影响，结果发现：（１）孤子能级偏离了禁带中心，能谱的对称性被破坏。（２）局域振动模发生劈裂，劈裂后两模的振动位形具有与原模相同的结构，但它们的频率和最大振幅均不同于原局域模。另外，模的频率还与两条链上的孤子类型以及链的相对序列有关。 关键词：     

一维单原子链中杂质引起的局域振动模

讨论了一维单原子链中杂质引起的晶格局域振动模和局域振动图像,分析了杂质质量和杂质近邻力常数对振动模的影响,通过数值求解晶格振动运动方程组．给出了局域振动模关于杂质质量和杂质近邻力常数分布的相图;分析了含杂质晶格振动模频率相对于完整晶格振动模频率的变化。     

荷电孤子的电子束缚态

现有理论认为聚乙炔中的孤子只具有一个电子束缚态——midgap态。本工作发现,由于电子之间存在相互作用,且高分子链具有分立的原子结构,荷电孤子在能隙中应具有两个电子束缚态:一个是深能级,它离能隙中央0.2eV;一个是浅能级,离带边0.06eV。反式聚乙炔的光致吸收光谱证实了此理论。 关键词：     

一维无序二元固体中电子局域性质的研究

从单电子紧束缚模型的哈密顿量出发，格点能量随机取ε_A和ε_B，只计及格点之间的近程跳跃积分，建立了一维无序二元固体模型. 利用负本征值理论及无限阶微扰理论，对系统电子的本征值和本征态进行了数值计算. 结果表明与一定能量本征值对应的电子波函数只分布在系统的一定范围内，显示了其局域性. 借助传输矩阵方法，计算出电子的局域长度，讨论了局域长度随本征能量和无序度的变化关系，并研究了计入不同范围跳跃积分下，局域长度的变化特征. 关键词： 无序 二元固体 电子态 局域长度     

聚乙炔孤子的二维局域振动模及其键弯曲势的影响

本文考虑了反式聚乙炔的平面结构,在二维空间内研究了孤子的局域振动模,并在此基础上讨论了键弯曲势对孤子局域模的影响,结果发现:1)晶格在垂链方向的振幅与链向的可比拟;2)当耦合参数λ取定值时,产生新的局域模(与SSH模型比较),且局域模的数目随着键弯曲势参数K的增加而增多,其局域性也随之增强。 关键词：     

非局域高次非线性介质中的多极暗孤子

研究一维非局域三-五次非线性模型下,暗孤子和多极暗孤子的新解和传输特性.发现非局域程度和非线性参量变化对暗孤子的峰值和束宽产生影响,并且在特定的竞争非局域非线性参数下存在稳定基态暗孤子和多极暗孤子的束缚态.另外,讨论了在局域自聚焦三次和非局域自散焦五次非线性介质中暗孤子和两极暗孤子的传输特性,发现孤子比在自散焦三次和自聚焦五次的非线性介质中传输更加稳定.进一步研究了单暗孤子和三极暗孤子的功率与传播常数和非局域程度的关系,并讨论了不同类型暗孤子的线性稳定性问题.     

Effects of the second and third neighbor hopping interactions on the electronic states of soliton in polyacetylene

We have studied the energy spectra and the electronic states of a soliton in the weakly coupled electron-phonon systems using an extension of SSH model that includes non-nearest neighbor hopping interactions. The results show that: (1) the electron-hole symmetry of the energy band structure implied by SSH model is broken, and the energy gap 2 increases. (2) for a negative charged soliton, only two bound states have been found, one of them is the midgap state, another is a new shallow state near the bottom of the conduction band; for a neutral soliton, all three bound states exist as in the SSH model, but their localizations are strengthened; for a positive charged soliton, four bound states have been found, one of which is an additional state near the top of the conduction band.     

Localized vibrational modes around solitons in coupled trans-polyacetylene chains

The effects of interchain coupling have been studied on the localized vibrational modes around a soliton in doped and photoexcited samples of trans-(CH)_x by using an extension of the SSH model in which two neighboring chains modeled individually by SSH Hamiltonian and coupled by an interchain electronic transfer term are considered. The electronic pinning is also included within this model. The localized modes obtained in the SSH model are split and their frequencies are shifted after turning on the interchain coupling. Furthermore, our result can account for the three strong infrared lines at 900, 1260 and 1370 cm^?1 along with a weaker peak at 1150 cm^? r in the optical absorption spectra of lightly doped samples.     

The vibrational modes around the soliton lattice with next neighbor hopping interactions in highly doped trans-(CH) x

Starting from the extended SSH model that includes an external Coulomb potential arising from interchain charged solitons and counterions, the intrachain e-e interaction and the next neighbor hopping interactions, eight localized vibrational modes around the soliton lattice have been found for the doping levels from 3.33 at.% to 13.33 at.%. Among them three are infrared active and they can be used to interpret the three observed infrared absorption lines at 487, 1284 and 1362 cm^–1. Furthermore, the frequencies of localized modes are decreased and their localizations are weakened when the dopant concentrations increase.     

THE 2D LOCALIZED MODES OF BIPOLARON IN cis-POLYACETYLENE

The localized vibrational modes around a bipolaron in cis-(CH)_x are studied by using a two-dimensional extension of the SSH model that includes the bond-bending term. A number of additional modes have been found, compared with the results based on the standard SSH model The amplitudes of the two directions (x and y direction) are comparable for most of the modes as in the trans-(CH)_x case. The number of localized modes and their frequencies depend not only on the coupling constant, but also on the bond-bending term and the parameter t₁ in removing the degeneracy of the ground state.     

Novel multi-band quantum soliton states for a derivative nonlinear Schrödinger model

We show that localized N-body soliton states exist for a quantum integrable derivative nonlinear Schrödinger model for several nonoverlapping ranges (called bands) of the coupling constant η. The number of such distinct bands is given by Euler's φ-function which appears in the context of number theory. The ranges of η within each band can also be determined completely using concepts from number theory such as Farey sequences and continued fractions. We observe that N-body soliton states appearing within each band can have both positive and negative momentum. Moreover, for all bands lying in the region η>0, soliton states with positive momentum have positive binding energy (called bound states), while the states with negative momentum have negative binding energy (anti-bound states).     

Effects of the Bond-Bending Term and e-e Interactions on the 2D Localized Modes Around a Polaron in Trans-Polyacetylene

The 2D localized modes of trans-(CH)_x around a polaron have been studied using a twodimensional extension of the SSH model that includes the bond-bending effect and the electron-electron interactions. The results show that 1) a number of additional localized modes have been found, which depend on the bond-bending term; 2) the number oflocalized modes does not change after turning on the e-e interactions, but their frequencies have been moved and the localization has been strengthened.     

Internal Modes of Relativistic Solitons

We apply a linear perturbation analysis to investigate the relationship between soliton oscillations and the integrability of nonlinear PDEs in bi-dimensional spacetime. For this purpose, we consider a localized solution of the nonlinear differential equation, and study small amplitude fluctuations around it. The linearized equation is a Schrödinger-like, eigenvalue problem. By considering several nonlinear PDEs, which are known to have soliton and solitary wave solutions, we find that in systems which are integrable, this eigenvalue equation has one and only one bound state with zero frequency. Non-integrable equations—in contrast—show extra bound states. The time evolution of the oscillations are also calculated, using a numerical program to integrate the time-dependent equation. The behavior of the modes are studied, using the Fourier transform of the evolving solutions.