Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

含时谐振子的动力学演化

利用含时量子变换理论,由量子变换理论中的变换矩阵,方便地给出了含时谐振子的演化算符,从而求得了含时谐振子的精确解. 关键词： 含时谐振子 含时量子变换 动力学演化     

Separation of Variable Treatment for Solving Time—Dependent Potentials

We use the separation of variable treatment to treat some time-dependent systems,and point out that the condition of separability is the same as the condition of existence of invariant,and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method.We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthen potential.     

Controlling Soliton Collisions of Condensates by Time-Dependence of Both Interactions and External Potential

Considering time-dependence of both interactions and external potential, we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation. It is found that for a closed external potential, the soliton-soliton distance is decreased with nonlinearly increased interactions, while the amplitude of each soliton increases and its width decreases. For linearly increased interactions but nonlinearly decreased external potential, especially, the atom transfer between two solitons is observed, different from previous theory of no atom transfer in solitons collision in a fixed external potential. In addition, it is shown that the collisional type, such as head-on,"chase", or collision period between two solitons, can be controlled by tuning both interactions and external potential. The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.     

Electronic Excitations in Pyrrole: A Test Case for Determination of Chromophores in the Chromogenic Effects of Neurotoxic Hydrocarbons by Time-Dependent Density Functional Theory and Single-Excitation Configuration Interaction Methods

Time-dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) calculations on the electronic excitations in pyrrole have been performed to examine the reliability of these first-principles electronic structure methods in predicting electronic excitation spectraof pyrrole-containing compounds. Both the TD-DFT and CIS calculations led to satisfactory results when compared to available experimental data, particularly for low-lying excited states. The TD-DFT and CIS calculations provide lower and upper limits of the excitation energies, respectively, for low-lying singlet excited states. These results suggest that these methods can be used for the prediction of the excitation spectra, particularly the excitation energies for low-lying excited states, of chromophores responsible for the chromogenic effects of neurotoxic hydrocarbons, which are believed to be substituted pyrroles and their adducts with proteins. As an example of a practical application, the spectrum of the widely used 2,5-dimethylpyrrole has been calculated. It is shown that the 2,5-dimethylpyrrole molecule does not have an absorption in the region of the visible spectrum (400-700 nm), suggesting that the absorption observed at 530 nm and the color of 2,5-dimethylpyrrole is due to another species, probably a product of possible 2,5-dimethylpyrrole autoxidation. This suggests that the conclusions from previously reported experimental studies of biochemical reactions of neurotoxic γ-diketones need to be reexamined in terms of the relationship of chromogenicity to neurotoxicity.     

含时耦合谐振子体系的动力学演化

利用含时量子变换理论,给出含时双模耦合谐振子的严格解.并根据这一结果,对于给定的初态为Fock态和相干态情形,讨论了其动力学演化.     

A time-dependent Fourier grid Hamiltonian-based formulation of time-dependent multi-configuration Hartree method

We propose a variant of the time-dependent multi-configuration Hartree method within the framework of Fourier grid Hamiltonian method. The workability of the method proposed is demonstrated with a well-known coupled two-mode problem.     

数值求解三维含时Schrodinger方程及其应用

发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrodinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高.

Abstract：

We present an accurate and effective pseudospectral method for solving the three-dimensional time-dependent Schrodinger equation involving the Coulomb potential. In this method, the Hamiltonian is evaluated by exploiting the two representations of the wave function. One is a grid representation, in which the angular dependence of the wave function is expanded in a two-dimensional Gauss-Legendre-Fourier grid in the coordinate space of polar and azimuthal angles. The radial coordinate is discretized using a discrete variable representation constructed from the Coulomb wave function (CWDVR) . The other is a spectral representation, in which the wave function is expanded in a set of square integrable functions chosen as the eigenfunctions of a zero-order Hamiltonian. The time of propagation of the wave function is calculated using the well-known second-order split-operator method implemented through the transform between the grid and spectral representations. Calculations on the photo-absorption strength of hydrogen atom are presented to demonstrate the accuracy of present method in low energy limit by the time-dependent wave-packet propagation method. As another example, the present method is applied to multiphoton ionization of H atom. For a wide range of field parameters, ionization rates calculated using the present method are in excellent agreement with those from other accurate numerical calculations. The new algorithm will be found more efficient than the close coupled wave packet method using CWDVR and/or methods based on evenly spaced grids.     

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.     

Phase shift of the population oscillation and population trapping

Using our recently developed time-dependent multilevel approach, we have calculated the phase shift of the population oscillation of the excited potassium atom in frequency-modulated fields when the modulation amplitude is suddenly changed. The numerical results are in good agreement with the measurements. A new way of realizing population trapping is suggested.     

Time Evolution in Macroscopic Systems. II. The Entropy

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined unambiguously, but it is the time derivative or entropy production that governs ongoing processes in these systems. The differences in physical interpretation and thermodynamic role of entropy in equilibrium and nonequilibrium systems is emphasized and the observable aspects of entropy production are noted. A basis for nonequilibrium thermodynamics is also outlined.     

Time Evolution in Macroscopic Systems. I. Equations of Motion

Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix (t). Because contains both classical and quantum-mechanical probabilities it is necessary to account for changes in both in the presence of external influences, yet standard treatments tend to neglect the former. A model of time-dependent classical probabilities is presented to illustrate the required type of extension to the conventional time-evolution equation, and it is shown that such an extension is already contained in the definition of the density matrix.     

极性染料溶液的微微秒动态荧光光谱移位

本文测量了染料分子DCM、甲酚紫、DODCI和DTDCI在极性溶剂中的微微秒时间分辨荧光光谱;作者将动态的光谱移位归结为由于溶质分子激发态与基态偶极矩的显著差异而引起的周围溶剂分子的介电弛豫;并从动态的光谱移位得到的弛豫时间很接近由连续腔体理论模型求得的计算值,表明连续胜体模型用于描述动态的光谱移位现象是适用的.     

One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach

Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x ^2j 〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.     

数值求解三维含时Schr?dinger方程及其应用

发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrdinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高. 关键词： 三维含时Schrdinger方程 库仑奇点 强场 含时波包传播     

关于含时不变量的一些普遍性质

讨论了量子力学中含时不变量的一些普遍性质,其中有些是文献中未曾提及的．     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释.通过分析文中的直观图像,研究了波包的动力学过程.结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的.     

含时阻尼线性谐振子的量子不变量处理

在适当的正则化变换下,采用Lewis-Riesenfeld量子不变量理论,得到了含时阻尼线性谐振子的精确波函数,波函数的正确性和普遍性同样得到讨论.     

Li2分子含时波包动力学的理论研究

利用含时量子波包方法计算得到了Li2分子的光电子能谱,并运用波包动力学理论对含有不同参量的光电子能谱现象给出了合理的解释。通过分析文中的直观图像,研究了波包的动力学过程。结果表明,泵浦-探测脉冲的延迟时间对光电子能谱的形状有重要的影响;在较短延迟时间下,能谱独特的四峰现象是由光诱导势的产生引起的。     

The effective use of precision electroweak measurements

Bound state population dynamics in a diatom modelled by an appropriate Morse oscillator with a time-dependent well-depth is investigated perturbatively both in the absence and presence of high intensity radiation. For sinusoidally oscillating well-depth, the population of themth bound vibrational level,P _mm(t), is predicted to be a parabolic function of the amplitude of the oscillation of the well-depth (ΔD ₀) at a fixed laser intensity. For a fixed value of ΔD ₀,P _mm(t) is also predicted to be quadratic function of the field intensity (ɛ ₀). Accurate numerical calculations using a time-dependent Fourier grid Hamiltonian (TDFGH) method proposed earlier corroborate the predictions of perturbation theory. As to the dissociation dynamics, the numerical results indicate that the intensity threshold is slightly lowered if the well-depth oscillates. Possibility of the existence of pulse-shape effect on the dissociation dynamics has also been investigated.