Nonlinear Lattice Effect on Ground State of One-Dimensional Electron-Phonon System

We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.     

抛物势量子点中强耦合双极化子量子比特的性质

基于LLP幺正变换,采用Pekar型变分法得到了二维量子点中强耦合双极化子的基态和第一激发态的能量和波函数,进而构造了一个双极化子的量子比特。数值结果表明:在量子比特内,两电子的空间几率密度的时间振荡周期T0随电声子耦合强度α、量子点的受限强度ω0以及介质的介电常数比η的增加而减小;在量子比特内,两电子的空间几率密度Q随时间t、角坐标φ2及介电常数比η的变化而作周期性振荡;两电子在量子点中心附近区域出现的几率较大,而在远离量子点中心区域出现的几率很小。     

Effect of Parabolic Potential on Bipolaron

We apply a Feynman path-integral variational approach combining with the average for the relative motion to study the stability of bipolaron in a quantum dot. The binding energy is calculated in different parameters. We find that an optimum quantum potential favors the formation of bipolaron. Compared with other methods in literature, the present approach is better than Laudau Pekar one in all coupling regime and full path-integral one in the strong coupling regime.     

Effect of Parabolic Potential on Bipolaron

We apply a Feynman path-integral variational approach combining with the average for the relative motion to study the stability of bipolaron in a quantum dot. The binding energy is calculated in different parameters. We find that an optimum quantum potential favors the formation of bipolaron. Compared with other methods in literature, the present pproach is better than Laudau-Pekar one in all coupling regime and full path-integral one in the strong coupling regime.     

Electron-Phonon Interaction in an Annular Quantum Dot

The confined longitudinal-optical （LO） phonon and surface-optical （SO） phonon modes of a free-standing annular cylindrical quantum dot are derived within the framework of dielectric continuum approximation. It is found that there exist two types of SO phonon modes： top SO （TSO） mode and side SO（SSO） mode in a cylindrical quantum annulus. Numerical calculation on CdS annulus system has been performed. Results reveal that the two different solutions of SSO mode distribute mainly at the inner or outer surfaces of the annulus. The dispersion relations and the coupling intensions of phonons in a quantum annulus are compared with those in a cylindrical quantum dot. It is found that the dispersion relations of the two different structures are similar, but the coupling intension of the phonon-electron interaction in quantum annulus is larger than that in quantum dot. The Hamiltonians describing the free phonon modes and their interactions with electrons in the system are also derived.     

二维Dilaton引力模型中的带电Sine–Gordon孤子解

获得了二维dilaton引力模型中的周期解,通过坐标变换证明了周期解和带电sine Gordon孤子解的等价性     

慢布拉格类孤子的传播特性

在耦合模理论的基础上，分析了线性周期结构的色散关系，给出了一维无限长的克尔类非线性介质周期结构中的慢布拉格类孤子解。并且指出，增加脉冲能量会导致群速度色散效应增强，在非线性作用下，禁带宽度会变小，波的频率也会发生偏移，其偏移量主要取决于失谐因子、传播速度、波振幅强度以及非线性系数等参量。     

Effect of the Electron—Phonon Coupling on Barrier D^— Quantum Dots in Magnetic Fields

The influence of the electron-phonon coupling of the energy of low-lying states of the barrier D^- center,which consists of a positive ion located on the z-azis at a distance from the two-dimensional quantum dot plane and two electrons in the dot plane bound by the ion,is investigated at arbitrary strength of maguetic field by mading use of the method of few-body physics.Discontinuous ground-state energy transitions induced by the magnetic field are reported.The dependence of the binding energy of the D^- ground state on the quantum dot radius is obtained.A considerable enhancement of the binding is found for the D^- ground state,which results from the confinement of electrons and electron-phonon coupling.     

Effects of Electron-Phonon Interaction on Linear and Nonlinear Optical Absorption in Cylindrical Quantum Wires

The electron-phonon interaction influences on lineax and nonfineax optical absorption in cylindrical quantum wires （CQW） with an infinite confining potential axe investigated. The optical absorption coefficients are obtained by using the compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs CQW. The results show that the electron-phonon interaction makes a distinct influence on optical absorption in CQW. The electron-phonon interaction on the wave functions of electron dominates the values of absorption coefficients and the correction of the electron-phonon effect on the energies of the electron makes the absorption peaks blue shift and become wider. Moreover, the electron-phonon interaction influence on optical absorption with an infinite confining potential is different from that with a finite confining potential.     

Optical Conductivity of Graphene Sheet Including Electron-Phonon Interaction

Using an expression of optical conductivity,based on the linear response theory,the Green's function technique and within the Holstein Hamiltonian model,the effect of electron-phonon interaction on the optical conductivity of graphene plane is studied.It is found that the electron-phonon coupling increases the optical conductivity of graphene sheet in the low frequency region due to decreasing quasiparticle weight of electron excitation while the optical conductivity reduces in the high frequency region.The latter is due to role of electrical field's frequency.     

Propagating Optical Phonon Modes and Their Electron-Phonon Interaction Hamiltonians in Asymmetric Wurtzite Nitride Semiconductor Quantum Wells

Within the framework of the dielectric continuum model and Loudon's uniaxial crystal model, the properties of frequency dispersion of the propagating (PR) optical phonon modes and the coupling functions of electron-PR phonons interaction in an asymmetrical wurtzite quantum well (QW) are deduced and analyzed via the method of electrostatic potential expanding. Numerical calculation on an asymmetrical Al_0.25Ga_0.75 N/GaN/Al_0.15Ga_0.85N wurtzite QW were performed. The results reveal that there are infinite branches of PR phonon modes in the systems. The behaviors of frequency forbidden of PR modes in the asymmetric QWs have been clearly observed. The mathematical and physical origins for these features have been analyzed in depth. The PR optical phonon branches have been distinguished and labelled reasonably in terms of the oscillating properties of the PR modes in the well-layer material. Moreover, the amplitudes and frequency properties of the electron-PR modes coupling functions in the barrier and well materials have also been analyzed from both of the mathematical and physical viewpoints.     

磷化物三元混晶中电子-声子相互作用的维度和体积效应

考虑电子-声子耦合强度因维度而异,导出了描述三维、二维和一维混晶中电子-声子相互作用的哈密顿量。考虑构成三元混晶的两种二元晶体的晶格失配会使混晶体积随元素组分比改变,在推导三维、二维和一维三元混晶中极化子自陷能量和重整化有效质量时计入了离子相对位移与二元晶体原胞体积的关系。结果表明:磷化物三元混晶中极化子自陷能量和重整化有效质量随元素组分的变化关系呈明显的非线性特征,对晶格适配明显、电子-声子耦合较强的材料,体积效应不可忽略。维度越低,非线性特征和体积效应越明显。     

Effects of Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.     

Improved Ligand-Field Theory with Effect of Electron-Phonon Interaction

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R₃', R₂', and R₁' lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG:Cr³⁺ as well as thermal shifts of GSZFS, R₁ line and R₂ line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R₁ line and R₂ line of ruby, several conclusions have also been obtained.     

Solitons in the Two-Dimensional Antiferromagnetic Heisenberg Model

An effective Hamiltonian of the two-dimensional antiferromagnetic Heisenberg model is derived by using the Holstein-Primakoff transformation. Three nonlinear coupled partial equations of motion are obtained. In the long-wavelength approximation, these equations, are reduced to the envelope function equations by the method of multiple scales. The amplitude functions satisfy the nonlinear Schrodinger equation. Introducing an inverse scatteriag transformation, the single-, two- and multi-soliton solutions in the two-dimensional antiferromagnetic Heisenberg model are investigated.     

Pressure-Induced Shift of R-Line of MgO:Cr3+ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the "pure electronic" pressure-induced shift (PS) and the PS due to electron-phonon interaction (EPI) of R-line of MgO:Cr3 have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO:Cr3 and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO:Cr3 and that of R1-line PS of ruby has been made.     

Pressure-Induced Shift of R-Line of MgO：Cr^3＋ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the ＂pure electronic＂ pressure-induced shift （PS） and the PS due to electron-phonon interaction （EPI） of R-line of MgO：Cr^3＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO：Cr^3＋ and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO：Cr^3＋ and that of R1-line PS of ruby has been made.     

Soliton-Like Solutions for the (2+l)-Dimensional Nonlinear Evolution Equation

By using a homogeneous balance method, we give new soliton-like solutions for the (2+1)-dimensional KdV equation and the (2+1)-dimensional breaking soliton equation. Solitary wave soIutions are shown to be a special case of the present results.     

New Exact Solutions of the N-Coupled Nonlinear Schroedinger System

In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.     

The Exact Solutions of Some (2 + 1)-Dimensional Integrable Systems

The equivalence of three (2 1)-dimensional soliton equations is proved, and the quite generalsolutionswitha some arbitrary functions of x, t and y respectively are obtained. By selecting the arbitrary functions, many specialtypes of the localized excitations like the solitoff solitons, multi-dromion solutions, lump, and multi-ring soliton solutionsare obtained.