Solution for One-Dimensional Quantum Oscillator with Time-Dependent Frequency and Mass

Based on the generalized linear quantum transformation theory, we present a normal ordering evolution operator for onedimensional quant urn oscillator with time-dependent frequency and mass, then give the exact expression of the evolution matrix elements, wave function and expectation value of arbitrary observable.     

含时调制的Jaynes-Cummings模型的Pancharatnam相位

基于含时调制的Jaynes-Cummings模型的SU(2)群结构,求得它的Pancharatnam相位,并分析 了该模型从绝热开启直到关闭原子与场的相互作用的整个过程的相位变化.讨论了该模型在 半经典近似条件下的情况. 关键词： 含时调制的Jaynes-Cummings模型 Pancharatnam相位 SU(2)群     

Chemistry of Spontaneous Alkylation of Methimazole with 1,2-Dichloroethane

Spontaneous S-alkylation of methimazole (1) with 1,2-dichloroethane (DCE) into 1,2-bis[(1-methyl-1H-imidazole-2-yl)thio]ethane (2), that we have described recently, opened the question about its formation pathway(s). Results of the synthetic, NMR spectroscopic, crystallographic and computational studies suggest that, under given conditions, 2 is obtained by direct attack of 1 on the chloroethyl derivative 2-[(chloroethyl)thio]-1-methyl-1H-imidazole (3), rather than through the isolated stable thiiranium ion isomer, i.e., 7-methyl-2H, 3H, 7H-imidazo[2,1-b]thiazol-4-ium chloride (4a, orthorhombic, space group Pnma), or in analogy with similar reactions, through postulated, but unproven intermediate thiiranium ion 5. Furthermore, in the reaction with 1, 4a prefers isomerization to the N-chloroethyl derivative, 1-chloroethyl-2,3-dihydro-3-methyl-1H-imidazole-2-thione (7), rather than alkylation to 2, while 7 further reacts with 1 to form 3-methyl-1-[(1-methyl-imidazole-2-yl)thioethyl]-1H-imidazole-2-thione (8, monoclinic, space group P 2₁/c). Additionally, during the isomerization of 3, the postulated intermediate thiiranium ion 5 was not detected by chromatographic and spectroscopic methods, nor by trapping with AgBF₄. However, trapping resulted in the formation of the silver complex of compound 3, i.e., bis-{2-[(chloroethyl)thio]-1-methyl-1H-imidazole}-silver(I)tetrafluoroborate (6_, monoclinic, space group P 2₁/c), which cyclized upon heating at 80 °C to 7-methyl-2H, 3H, 7H-imidazo[2,1-b]thiazol-4-ium tetrafluoroborate (4b, monoclinic, space group P 2₁/c). Finally, we observed thermal isomerization of both 2 and 2,3-dihydro-3-methyl-1-[(1-methyl-1H-imidazole-2-yl)thioethyl]-1H-imidazole-2-thione (8), into 1,2-bis(2,3-dihydro-3-methyl-1H-imidazole-2-thione-1-yl)ethane (9), which confirmed their structures.     

Predicting the wind noise from the pantograph cover of a train

Finite element and boundary element calculations are combined to predict the flow noise radiated from a 1/10th-scale model of an aerodynamic cover used around the pantograph on a train at 250 km h⁻¹. The solutions of the unsteady air flow over the cover and the resulting sound propagation are divided into two parts in order to keep the problem tractable. First the unsteady fluid flow is solved using large-eddy simulation (LES). The pressure histories on the cover are then used to predict the radiated sound, using a boundary element method to solve the Helmholtz equation. The result thus leans heavily on assumptions about the coupling of the two solutions, the propagation of sound in a disturbed medium and the efficacy of LES. The predicted sound pressure levels are compared with experimental measurements made in an anechoic wind tunnel. © 1997 John Wiley & Sons, Ltd.     

Optical Spectra of Oligofurans: A Theoretical Approach to the Transition Energies,Reorganization Energies,and the Vibronic Activity

There is experimental evidence of high vibronic activity that accompanies the allowed transition between the ground state and the lowest electronic singlet excited state of oligofurans that contain two, three, and four furan rings. The absorption and emission spectra of the three lowest oligofurans measured at liquid nitrogen temperature show distinct fine structures that are reproduced using the projection-based model of vibronic coupling (with Dushinsky rotation included) parameterized utilizing either Density Functional Theory (DFT, with several different exchange-correlation functionals) or ab initio (CC2) quantum chemistry calculations. Using as a reference the experimental data concerning the electronic absorption and fluorescence for the eight lowest oligofurans, we first analyzed the performance of the exchange-correlation functionals for the electronic transition energies and the reorganization energies. Subsequently, we used the best functionals alongside with the CC2 method to explore how the reorganization energies are distributed among the totally symmetric vibrations, identify the normal modes that dominate in the fine structures present in the absorption and emission bands, and trace their evolution with the increasing number of rings in the oligofuran series. Confrontation of the simulated spectra with the experiment allows for the verification of the performance of the selected DFT functionals and the CC2 method.     

Secondary plasmon resonance in graphene nanostructures

The plasmon characteristics of two graphene nanostructures are studied using time-dependent density functional theory (TDDFT). The absorption spectrum has two main bands, which result from π and σ + π plasmon resonances. At low energies, the Fourier transform of the induced charge density maps exhibits anomalous behavior, with a π phase change in the charge density maps in the plane of the graphene and those in the plane 0.3 ? from the graphene. The charge density fluctuations close to the plane of the graphene are much smaller than those above and beneath the graphene plane. However, this phenomenon disappears at higher energies. By analyzing the electronic properties, we may conclude that the restoring force for the plasmon in the plane of the graphene does not result from fixed positive ions, but rather the Coulomb interactions with the plasmonic oscillations away from the plane of the graphene, which extend in the surface-normal direction. The collective oscillation in the graphene plane results in a forced vibration. Accordingly, the low-energy plasmon in the graphene can be split into two components: a normal component, which corresponds to direct feedback of the external perturbation, and a secondary component, which corresponds to feedback of the Coulombic interaction with the normal component.     

PTCDA分子基态的飞秒激光控制研究

将优化控制理论和多组态含时Hartree（MCTDH）方法相结合,建立了适合于MCTDH方法的计算具有平面结构的PTCDA分子的多自由度振动量子模型,研究了在PTCDA分子激发后从分子激发态回落至分子基态的动力学过程.在理论上分析了约化目标态产生率与激发脉冲、分子的演变时间及优化场的有效能量之间的关系,对分子在各个振动坐标下波函数的振动分布做了分析与比较.研究发现,增加分子的回落演变时间在提高目标态产生率的同时可以使优化激光控制场的强度降低,这为实验上用低能量激光最大程度地实现目标态提供了有效手段. 关键词： PTCDA 多组态含时Hartree方法 飞秒激光控制     

有源介观LC电路的量子涨落

本文利用含时微扰论,研究了电源幅值较小时介观LC电路中电荷与电流的量子涨落。在确定的温度下,系统将处在混合态,进一步得到有限温度下含源介观LC电路的量子涨落。研究表明有源介观LC电路的量子涨落不仅与电路参数有关,还与时间和温度有关。     

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.     

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