Analytic Results in the Position-Dependent Mass SchrSdinger Problem

We investigate the Schr6dinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the （nontrivial） position-dependent mass V（x） = 0 case whose solutions are hypergeometric functions in tanh2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstat, es for a potential of the form V （x） = Vo sinh2 z.     

Chaos control in the nonlinear Schrodinger equation with Kerr law nonlinearity

The nonlinear Schr6dinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.     

A new finite difference scheme for a dissipative cubic nonlinear Schr6dinger equation

This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.     

Novel exact solutions of coupled nonlinear Schrōdinger equations with time-space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.     

A proposed method to characterize high harmonic microbunching in EEHG operation of SDUV-FEL

The echo-enabled harmonic generation （EEHG） scheme offers remarkable efficiency for generating high harmonic microbunching with a relatively small energy modulation. A proof of principle experiment of the EEHG scheme has been proposed at the Shanghai deep ultraviolet （SDUV） free electron laser （FEL） facility, where the 4th harmonic of the seed laser is amplified in the 9 m long radiator. To explore the advantages of the EEHG scheme, in this paper, a method of measuring the coherent high harmonic radiation of the radiator is proposed to investigate the electron beam microbunching corresponding to the 10th-20th harmonics of the seed laser. The principle of the proposed method, comparisons with existing methods and the simulation results are presented and discussed.     

A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

SU(1,1) Coherent States for Position-Dependent Mass Singular Oscillators

The Schr?dinger equation for position-dependent mass singular oscillators is solved by means of the factorization method and point transformations. These systems share their spectrum with the conventional singular oscillator. Ladder operators are constructed to close the su(1,1) Lie algebra and the involved point transformations are shown to preserve the structure of the Barut-Girardello and Perelomov coherent states.     

Mapping of the position-dependent mass Schroedinger equation under point canonical transformation

In this paper, the three-dimensional radial position-dependent mass Schroedinger equation is exactly solved through mapping this wave equation into the constant mass Schroedinger equation with Coulomb potential by means of point canonical transformation. The wavefunctions here can be given in terms of confluent hypergeometric functions.     

A conservative Fourier pseudospectral algorithm for the nonlinear Schrdinger equation

In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ｜｜·｜｜2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.     

原子薛定谔猫态中角动量的压缩及其时间演化

在低Q值腔内，原子相干态在一些特定时刻可以演化为原子薛定谔猫态.讨论了在这种原子薛定谔猫态中原子角动量的涨落和高阶涨落.根据不确定性原理，进一步研究了原子角动量的压缩和高阶压缩性质及其演化.研究表明，原子薛定谔猫态可以被压缩到二阶和六阶，但不能被压缩到四阶.当原子薛定谔猫态中被叠加的原子相干态数为无限多项时，其压缩特性与原子相干态相同. 关键词： 原子相干态 薛定谔猫态 角动量压缩 Bloch态     

Two-Photon Ionization of He through a Superposition of Higher Harmonics

We present experimental results and theoretical analysis of two-photon ionization of He by a superposition of the 7th to the 13th harmonic of a Ti:sapphire laser. Solving the time-dependent Schr?dinger equation for He in a coherent polychromatic field, the He+ yield is calculated. From this yield the number of He+ ions produced has been estimated and found in reasonable agreement with its measured value. The present results establish the feasibility of a second-order autocorrelation measurement of superposition of harmonics, and thus they represent the precursor towards the direct temporal characterization of attosecond pulse trains.     

An element-free Galerkin （EFG） method for numerical solution of the coupled Schrodinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrodinger-KdV equations using the elementfree Galerkin （EFG） method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method （FDM） and the finite element method （FEM）, this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.     

利用介观LC电路制备薛定谔猫态

提出了一种制备相干态的叠加态，即薛定谔猫态的方案. 该方案是基于将外加冲激信号作用于介观LC电路系统而设计的. 在该薛定谔猫态下，介观电路系统有非经典的量子压缩效应. 关键词： 介观LC电路 冲激信号 薛定谔猫态     

用explicit Euler 方法研究含时受迫谐振子的演化及对系统循环初态的讨论

利用Ioan Sturzu 提出的explicit Euler方法 (EEM) 计算了含时受迫谐振子的系统初态随时间的演化及概率分布规律，分析了EEM的可行性及适用性，并由相干态讨论了受迫谐振子系统循环初态的存在条件以及非绝热几何相. 关键词： explicit Euler 方法 含时受迫谐振子 循环初态 非绝热几何相     

双色场中氦离子高次谐波的保结构算法研究及应用

 通过数值求解含时Schr ö dinger方程,研究了氦离子在不同双色场下的高次谐波。结果显示,尽管倍频光强度仅为基频光的1/10,高次谐波辐射却发生了极大变化。虽然谐波级次推进不多,但效率大大提高了,平台区平均提高103倍,高倍频光对应的高次谐波产生效率提高104~105倍。氦离子在添加倍频光的双色场作用下高次谐波产生效率极大提高的原因是：倍频光极大地加快了电子电离到连续态及返回基态这一过程,使辐射出的高次谐波光子数大大增加,该初步阐释可为高次谐波真正应用到实际中提供一些理论启示。     

Laser phase control of high-order harmonic generation at large internuclear distance: the H+ -H2+ system

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schr?dinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.     

幂函数叠加势的径向薛定谔方程的解析解(英文)

当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,本文采用奇点邻域附近的级数解法与求解渐近解相结合并且通过系数比较法,得到势函数为V(r)=a1r6 a2r2 a3r-4 a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构,并作了适当讨论与结论.     

(2+1)维非线性薛定谔方程的环孤子,dromion,呼吸子和瞬子

利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸 关键词： 非线性薛定谔方程 分离变量法 孤子结构     

一维μ介子模型原子的超强场高次谐波发射

本文提出了一个一维μ介子原子模型,用数值积分方法求解了在超强激光场作用下该模型原子的含时Schrdinger方程,得到了它的高次谐波发射谱.该谱表明,借助于这一奇异原子模型,可将相干辐射由XUV波段推向γ-射线波段.针对这个体系的高次谐波发射效率低的缺点,引入双色场后使发射效率提高了两个数量级.     

用拉普拉斯变换得到N维谐振子的精确解

通过拉普拉斯变换可以把N维谐振子的Schr?dinger方程退化为一次微分方程，然后得到精确的束缚态解。结果显示这种求解Schr?dinger方程方法跟低维一样可以代替标准的函数分析方法。