有限格点一维Holstein极化子研究

利用相干态正交化展开法,得到了一维Holstein模型基态能量的解析表达式.为了便于比较,将系统的基态试探波函数逐级展开到三级近似,计算了不同格点、不同耦合强度下的基态能量,在展开到3级近似时,所得结果与数值计算一致. 关键词： 相干态正交化展开 极化子 模拟退火方法     

在相干态表象中精确求解无旋波近似的Jaynes-Cummings模型

在相干态表象中精确求解了无旋波近似的Jaynes-Cummings模型，并导出了相应的限制性条件．所求得的解析解与用微扰论求得的近似解比较，当微扰级数取无穷时所得结果一致．本文的方法能方便地推广到三能级系统的讨论． 关键词：     

非旋波近似下两纠缠原子的纠缠特性

采用了相干态正交化法研究了耦合强度以及偶极相互作用对Tavis-Cummings模型中两原子的纠缠的影响.与旋波近似比较发现,在弱耦合强度下,非旋波近似下两原子间的纠缠与旋波近似下的结果符合得很好,在强耦合区,原子之间的纠缠出现了突然死亡现象.研究同时发现耦合强度越大,原子间处于可分离态的时间越长,表明了原子间处于退纠缠的时间的长短是依赖于原子-光场的耦合强度的.而考虑了偶极相互作用时,随着偶极-偶极相互作用的加强,原子间的纠缠也将被加强.     

非旋波近似下两纠缠原子的纠缠特性

采用了相干态正交化法研究了耦合强度以及偶极相互作用对Tavis-Cummings模型中两原子的纠缠的影响.与旋波近似比较发现,在弱耦合强度下,非旋波近似下两原子间的纠缠与旋波近似下的结果符合得很好,在强耦合区,原子之间的纠缠出现了突然死亡现象.研究同时发现耦合强度越大,原子间处于可分离态的时间越长,表明了原子间处于退纠缠的时间的长短是依赖于原子-光场的耦合强度的.而考虑了偶极相互作用时,随着偶极-偶极相互作用的加强,原子间的纠缠也将被加强.     

两量子比特与谐振子相耦合系统中的量子纠缠演化特性

在非旋波近似下, 利用相干态正交化展开方法, 对两量子比特与谐振子相耦合系统中的量子纠缠演化特性进行了精确计算. 讨论了在共振时, 两量子比特和谐振子耦合系统基态的性质以及量子比特和谐振子之间的纠缠与量子比特-量子比特间的纠缠的不同. 结果表明: 当不考虑外场时, 量子比特-量子比特间的纠缠随着耦合强度的增大从1迅速地减小到零, 表明了量子比特-量子比特间的纠缠对耦合强度是非常敏感的; 而量子比特和谐振子之间的纠缠随着耦合强度的增大从零迅速地增大, 但不能达到理论上的最大值2; 当初始时刻两量子比特没有纠缠时, 在弱耦合强度下, 真空场不能导致纠缠的产生; 而强的耦合非旋波效应则可以导致纠缠的突然产生现象. 关键词： 相干态正交化展开 非旋波近似 量子纠缠     

非旋波近似下Tavis-Cummings模型的定态能谱和纠缠演化

利用相干态正交化展开法研究非旋波近似下Tavis-Cummings模型的定态能谱,以及模型中原子初态和耦合强度对系统纠缠度的影响.结果表明:系统的基态是非简并的,对应于两原子处于交换对称态.当两原子的初态处于交换反对称状态时,两原子间的纠缠能一直处于最大纠缠;在非旋波项的作用下,两原子初态处于非纠缠态时也能够产生周期性的纠缠.腔场与原子间的耦合强度对系统的演化有着重要作用.     

各向异性海森伯自旋链中的高阶孤子

在Holstain-Primakoff表象中研究了各向异性海森伯自旋链模型.在半经典近似条件下,应用相干态求出了明孤子和暗孤子的精确解析解.结果表明:这些解可以用第一类和第三类椭圆积分来表示.内容丰富的暗孤子解是本论文的创新之处.     

精确求解级联型三能级原子与单模相干态光场场熵的演化特性

本文利用全量子理论,在非旋波近似下对单模相干态光场与级联型三能级原子相互作用过程中场熵随时间的演化进行了精确求解.数值计算的结果表明：随着初始时刻平均光子数n以及光场与原子的耦合强度u, v的增大,场熵的平均值先增大后减小,因此纠缠度也同样先增大后减小;随着失谐量Δ的增大,场熵的平均值逐渐减小,因此纠缠度也逐渐减小. 关键词： 相干态正交化展开 非旋波近似 场熵     

非旋波近似下Λ型三能级原子与相干态光场的量子纠缠

在非旋波近似下,利用相干态正交化展开方法,对相干态光场与Λ型三能级原子相互作用的量子场熵进行了精确求解.利用量子熵理论讨论了耦合强度、平均光子数以及初始时刻原子处于不同的能级对量子纠缠的影响.数值计算的结果表明：当初始时刻原子处于激发态时,量子纠缠在较短的时间内就能演化到最大值,随着平均光子数的增大,纠缠演化的周期性逐渐明显|原子初始时刻处于三个能级的叠加态会使初始阶段量子纠缠显著降低|与旋波近似下的结果不同的是,随着耦合强度以及平均光子数的增加,非旋波项的贡献显著增强,使得量子纠缠演化曲线出现小锯齿状的振荡.     

非旋波近似下Λ型三能级原子与相干态光场的量子纠缠

在非旋波近似下,利用相干态正交化展开方法,对相干态光场与Λ型三能级原子相互作用的量子场熵进行了精确求解.利用量子熵理论讨论了耦合强度、平均光子数以及初始时刻原子处于不同的能级对量子纠缠的影响.数值计算的结果表明:当初始时刻原子处于激发态时,量子纠缠在较短的时间内就能演化到最大值,随着平均光子数的增大,纠缠演化的周期性逐渐明显;原子初始时刻处于三个能级的叠加态会使初始阶段量子纠缠显著降低;与旋波近似下的结果不同的是,随着耦合强度以及平均光子数的增加,非旋波项的贡献显著增强,使得量子纠缠演化曲线出现小锯齿状的振荡.     

A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation

A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.     

Exact Solutions to the Quantum Rabi-Stark Model Within Tunable Coherent States

The quantum Rabi-Stark model, where the linear dipole coupling and the nonlinear Stark-like coupling is present on an equal footing, is studied within the tunable extended coherent states. The eigenvalues and eigenstates are therefore obtained exactly. Surprisingly, the entanglement entropy in the ground-state is found to jump suddenly with the coupling strength. The first-order quantum phase transition can be detected by level crossing of the ground state and the first excited state, which is however lacking in the original linear quantum Rabi model. Performing the first-order approximation in the present theory, we can derive closed-form analytical results for the ground-state. Interestingly, it agrees well with the exact solutions up to the ultra-strong coupling regime in a wide range of model parameters. The spectral collapses when the absolute value of the nonlinear coupling strength approaches to twice the cavity frequency is observed with the help of new solutions in the limits.     

Application of the homotopy analysis method for the Gross-Pitaevskii equation with a harmonic trap

<正>The Homotopy analysis method(HAM) is adopted to find the approximate analytical solutions of the GrossPitaevskii equation,a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they fit very well with each other when the atomic interaction is weak.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking(OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity(QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Nonlinear Dust Acoustic Waves in Strongly Coupled Dusty Plasmas with Positively Charged Dust Particles

The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation.We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev–Petviashvili(KP) equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.     

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.     

Linear versus nonlinear coupling effects in single- and multiphonon atom-surface scattering

We present a comparative assessment of the features of inelastic atom-surface scattering spectra that are produced by different forms of linear and nonlinear phonon coupling to the projectile atom. Starting from a simple theoretical model of atom-surface scattering and employing recently developed exact numerical and approximate analytical methods we calculate and compare the scattering probabilities ensuing from each form of interaction. This enables us to demonstrate that in the regime of thermal energy atom scattering from surfaces the dominant contributions to the zero-, one-, and multiphonon excitation probabilities arise from linear coupling treated to all orders in the interaction.     

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.