引入反比相关双曲余弦平方势描述超晶格量子阱的电子跃迁

 鉴于“方形”势阱过于简单和理想，引入了反比相关双曲余弦平方势描述超晶格量子阱中的电子运动行为。在量子力学框架内，把电子的Schrodinger方程化为了超几何方程, 并以Ga^1-xAl^xAs-GaAs- Ga^1-xAl^xAs量子阱为例计算了电子的带内跃迁和带间跃迁。结果表明，能级数目和跃迁能量与阱深、阱宽等系统参数有关，只需适当调节这些参数就可望实现对超晶格量子阱光电特征的调节与控制。     

引入反比相关双曲余弦平方势描述超晶格量子阱的电子跃迁

鉴于“方形”势阱过于简单和理想,引入了反比相关双曲余弦平方势描述超晶格量子阱中的电子运动行为。在量子力学框架内,把电子的Schrodinger方程化为了超几何方程, 并以Ga1-xAlxAs-GaAs- Ga1-xAlxAs量子阱为例计算了电子的带内跃迁和带间跃迁。结果表明,能级数目和跃迁能量与阱深、阱宽等系统参数有关,只需适当调节这些参数就可望实现对超晶格量子阱光电特征的调节与控制。     

半导体超晶格量子阱研究

 自从1969年美国IBM公司的江畸(L.Esaki)和朱兆祥提出超晶格概念以来,半导体超晶格量子阱的研究巳成为半导体领域自40年代末单晶和晶体管问世以来所发生的最重大事件.这个研究领域之所以倍受重视,除了因为有明显的技术应用前景之外,还因为在物理上它提供了一个极好的、能在实验上观测量子尺寸效应的理想模型.     

含时微扰Schr(o)dinger方程的精确求解与量子跃迁

在有关量子跃迁的问题中,含时微扰理论给出了跃迁概率振幅的一级近似解．本文通过计算指出,若微扰只与时间有关,则体系的波函数可以精确求解,从而得到跃迁概率振幅的精确表达式。     

超晶格结构中电子的波动性

在温度T=77K,测量了GaAs/AlGaAs超晶格的光电流,观测到在ν=1589cm^-1有一个强电流峰,而在ν=1779,2129和2401cm^-1附近存在弱电流峰.分析认为,这些电流峰与电子的波动性有关.据电子波动理论计算出的光电流峰位置与实验测量结果相当一致 关键词： 超晶格 电子 波动性     

超晶格量子阱与现代物理的教学化

从超晶格材料的人工剪裁这一最富生命力的新兴边缘学科出发，分析了量子阱所诱发的新现象和复电容率的物理意义，探讨了有关学科横向交叉综合处如何体现现代物理的教学化的新途径。     

GaAs/AlGaAs Fibonacci准周期超晶格带间跃迁的光谱研究

运用光致荧光,光调制反射和光电流谱等方法研究了11级的GaAs/AlGaASFibonacci准周期超晶格的带间跃迁,并用转移矩阵方法计算了Fibonacci准周期超晶格和相应的周期性超晶格的子能级和子能带.理论计算与实验结果符合得很好. 关键词：     

含时微扰Schrdinger方程的精确求解与量子跃迁

在有关量子跃迁的问题中,含时微扰理论给出了跃迁概率振幅的一级近似解.本文通过计算指出,若微扰只与时间有关,则体系的波函数可以精确求解,从而得到跃迁概率振幅的精确表达式.     

室温下ZnS-ZnTe应变超晶格的带间跃迁

本文报导了ZnS-ZnTe应变超晶格中的载流子在室温下跃迁复合性质.通过测量室温下光致发光光谱,对载流子在超晶格带间跃迁的过程进行了研究.     

掺杂超晶格量子阱的沟道效应与沟道辐射

分析了超晶格量子阱的沟道效应和沟道辐射,利用正弦平方势描述了掺杂超晶格量子阱沟道粒子的运动行为,并在经典力学框架内,把粒子的运动方程化为摆方程。用Jacobian椭圆函数和椭圆积分解析地给出了系统的解和粒子运动周期,导出了量子阱沟道辐射的辐射强度和辐射能量。结果表明,对于能量为100 MeV左右的电子,辐射能量可达keV量级（X能区）。指出了用量子阱沟道辐射作为X激光或γ激光的可能性。     

Conformal structure-preserving method for damped nonlinear Schrdinger equation

In this paper,we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger(DNLS) equation.Based on its damped multi-symplectic formulation,the DNLS system can be split into a Hamiltonian part and a dissipative part.For the Hamiltonian part,the average vector field(AVF) method and implicit midpoint method are employed in spatial and temporal discretizations,respectively.For the dissipative part,we can solve it exactly.The proposed method conserves the conformal momentum conservation law in any local time-space region.With periodic boundary conditions,this method also preserves the total conformal momentum and the dissipation rate of momentum exactly.Numerical experiments are presented to demonstrate the conservative properties of the proposed method.     

变系数非线性Schrödinger方程的孤子解及其相互作用

在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrödinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrödinger方程转化成非线性Schrödinger方程,并利用已知解深入研究变系数非线性Schrödinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论. 关键词： 非线性Schrö dinger方程 相似变换 变系数 孤子解     

Localized waves in three-component coupled nonlinear Schrdinger equation

We study the generalized Darboux transformation to the three-component coupled nonlinear Schr ¨odinger equation.First-and second-order localized waves are obtained by this technique.In first-order localized wave,we get the interactional solutions between first-order rogue wave and one-dark,one-bright soliton respectively.Meanwhile,the interactional solutions between one-breather and first-order rogue wave are also given.In second-order localized wave,one-dark-one-bright soliton together with second-order rogue wave is presented in the first component,and two-bright soliton together with second-order rogue wave are gained respectively in the other two components.Besides,we observe second-order rogue wave together with one-breather in three components.Moreover,by increasing the absolute values of two free parameters,the nonlinear waves merge with each other distinctly.These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system.     

Exact solutions of the Schrödinger equation for a class of hyperbolic potential well

We propose a new scheme to study the exact solutions of a class of hyperbolic potential well. We first apply different forms of function transformation and variable substitution to transform the Schrödinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate. And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant, we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well. Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function. The linearly dependent relation between two eigenfunctions is also studied.     

Solitons for a generalized variable-coefficient nonlinear Schrdinger equation

In this paper,we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear Schrdinger equation (NLS) with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions,one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results,some previous one-and two-soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one-and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.     

含时Schrödinger方程的高阶辛FDTD算法研究

提出了一种新的算法——高阶辛时域有限差分法(SFDTD(3, 4): symplectic finite-difference time-domain)求解含时薛定谔方程.在时间上采用三阶辛积分格式离散, 空间上采用四阶精度的同位差分格式离散, 建立了求解含时薛定谔方程的高阶离散辛框架;探讨了高阶辛算法的稳定性及数值色散性.通过理论上的分析及数值算例表明:当空间采用高阶同位差分格式时, 辛积分可提高算法的稳定度;SFDTD(3, 4)法和FDTD(2, 4)法较传统的FDTD(2, 2)法数值色散性明显改善.对二维量子阱和谐振子的仿真结果表明: SFDTD(3, 4)法较传统的FDTD(2, 2)法及高阶FDTD(2, 4)法有着更好的计算精度和收敛性, 且SFDTD(3, 4)法能够保持量子系统的能量守恒, 适用于长时间仿真.     

Chaos control in the nonlinear Schrdinger equation with Kerr law nonlinearity

The nonlinear Schrdinger 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.     

Collapse arrest in the space-fractional Schrödinger equation with an optical lattice

The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schr?dinger equation with Kerr nonlinearity and optical lattice. The approximate analytical soliton solutions are obtained based on the variational approach, which provides reasonable accuracy. Linear-stability analysis shows that all the solitons are linearly stable. No collapses are found when the Lévy index 1 α≤ 2. For α = 1, the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough. It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schr?dinger equation still holds in the one-dimensional fractional Schr?dinger equation. The physical mechanism for collapse prohibition is also given.     

Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation

Rogue waves are a class of nonlinear waves with extreme amplitudes, which usually appear suddenly and disappear without any trace. Recently, the parity-time ($\mathcal {PT}$)-symmetric vector rogue waves (RWs) of multi-component nonlinear Schrödinger equation ($n$-NLSE) are usually derived by the methods of integrable systems. In this paper, we utilize the multi-stage physics-informed neural networks (MS-PINNs) algorithm to derive the data-driven $\mathcal {PT}$ symmetric vector RWs solution of coupled NLS system in elliptic and X-shapes domains with nonzero boundary condition. The results of the experiment show that the multi-stage physics-informed neural networks are quite feasible and effective for multi-component nonlinear physical systems in the above domains and boundary conditions.