Observation of quantum beat in Rb by parametric four-wave mixing

Two coupled parametric four-wave-mixing processed in Rb atoms are studied using perturbation theory, which reveals clear evidence of the appearance of quantum beat at 608 cm(-1), corresponding to the energy difference of the 7s - 5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Time-varying characteristics of the quantum beat are investigated using time-dependent Fourier transform. The results show that the time-varying characteristics of the quantum beat potential tool for monitoring the dissociation of molecules.

Identical dual-wavelength fiber Bragg Gratings

In this paper, identical dual-wavelength fiber Bragg, gratings (FBGs) are theoretically proposed and experimentally demonstrated. On the assistance of the Fourier theory, the gratings with symmetrical spectrum are designed in the case of weak refractive-index modulations. With the. perturbation technique, the results achieved in the previous step are modified to meet the strong refractive-index modulation gratings. Based on the coupled-mode theory, we have optimized and achieved the identical dual-wavelength FBGs with two channels that have equal bandwidth and even strength. We have also experimentally demonstrated the proposed FBGs, and the experimental results are compared with theoretical predictions with good agreement.

两个冠醚分子在简正坐标分析及NRCC程序在微机上的移植

本文用加拿大国立研究院(National Research Council of Canada) Fuhrer等人编制的FORTRAN语言程序（以下简称NRCC程序），对两个冠醚类化合物进行了简正坐标分析，这两个化合物分子是二氧六环(C_4H_8O_2)和12－冠－4(C_8H_(16)O_4)。作者用Synder和Zerbi提出的一般价力场，计算了二氧六环的36个简正振动频率，精化四次后的结果误差为14.04 cm~(-1)，得到了二氧六环的精化力场和势能分析矩阵；做了12－冠－4－的中红外光谱(3200-5000cm~(-1))。远红外光谱(500-70cm~(-1))和拉曼光谱(3200-50 cm~(-1)，从而归属出12－冠－4的78个简正振动频率实验值；利用二氧六环的精化力场作为初始力场，计算了12－冠－4的简正振动频率，对78个简正振动频率进行了精化计算，精化三次后的结果误差为13.99 cm~(-1)，精化后得到12－冠－4的精化力场和势能分布矩阵；将NRCC程序以BASIC语言移至TRS-80微型机上，对二氧六环进行了计算，结果良好，首次给出二氧六环一般价力场的势能分布。一、对二氧六环的处理 二氧六环分子式C_4H_8O_2，合14个原子，有3N－6＝36个简正振动频率。分子结构系由二个乙氧基(-CH_2-CH_2-O-)单元组成的含有四个碳，两个氧的六元环，平衡态分子为椅式构象，属于C_(2h)点群，36个简正振动频率分为四个对称类Ag、Au、Bg和Bu，分布是：Ag 10个，Bg 8个，Au 9个，Bu9个。二氧六环的分子结构及坐标示意图见28而图5，定义了14个伸缩内坐标，26个弯曲内坐标，6个扭曲内坐标，共46个，C－C键长1.54A，C-O键长1.41 A，C－H键长1.096A，键角都用109°28'。用CART程序（NRCC程序之一）计算二氧六环14个原子的笛卡尔坐标，用GMAT程序（NRCC程序之二）计算其B矩阵和G矩阵，用FPERT程序（NRCC程序之三）计算其简正振动频率、精化力场，计算用一般价力场，引入V矩阵对称化，将46个坐标化为46个（内）对称坐标，10个多余坐标在FPERT程序计算中除去。二、对12－冠－4的处理 12－冠－4分子式C_8H_(16)O_4，含28个原子，共3N－6＝78个简正振动频率，分子结构为四个乙氧基(-CH_2-CH_2-O-)单元组成的含八个碳、四个氧的12元环，自由分子的12－冠－4属于C点群。结构数据引自Groth的X光衍射分数和坐标，自己编制了BASIC语言程度将分数坐标化为笛卡尔坐标，用GMAT程序计算B矩阵和G矩阵，FPERT程序计算78个简正振动频率、精化力场、计算势能分布矩阵，引入U矩阵将92个内坐标化为92个对称坐标，14个多余坐标在FPERT程序中自动除去。三、结果 势能分布矩阵给出分子的振动归属，对这两个冠醚类分子的3N－6个简正振动频率，可以划分为五个振动区域。1．C－H伸缩振动区（3000－2800 cm~(-1)） 在该区中，二氧六环有八个值：2974、2966、2854和2867 cm~(-1)各两个，12－冠－4有16个值：2935、2923、2915和2907 cm~(-1)各两个，2860 cm~(-1)8个，高于2900 cm~(-1)者为反对称伸缩振动，低于2900 cm~(-1)者为对称伸缩振动。2．亚甲基弯曲振动之一(1500-1400 cm~(-1)) 该区的主要振动是亚甲基剪式振动(Scissor)，其它振动小于10％二氧六环在该区有四个频率：1443、1461、1451和1457 cm~(-1)，12－冠－4有八个频率：1466、1450、1450和1405 cm~(-1)各两个。3．亚甲基弯曲振动区二(1400-1200 cm~(-1))该区的主要振动模式为亚甲基的颤动(wag)、卷曲(twist)和摆动(rock)振动，其它振动小于13％。二氧六环在该区有八个频率：1334、1303、1396、1216、1367、1264、1377和1296 cm~(-1)，12－冠－4有十六个频率：1388、1363、……1229 cm~(-1)（其中1288、1307cm~(-1)非简并，其余皆两重简并）。4．环的骨架伸缩振动区(1200-600 cm~(-1))该区振动模式复杂，除环的骨架伸缩振动外，还有亚甲基的wag、twist、rock以及环的骨架弯曲振动，而且这些振动的势能分布值都不小。二氧六环在该区有十一个频率，从1127至610 cm~(-1)，12－冠－4有二十个频率，从1135至184 cm~(-1)且大都是二重简并的。5．低频区(600-50cm~(-1))这两个分子在低频区的势能分布略有差别。二氧六环在该区有五个频率：503、486、427、276和224 cm~(-1)，主要振动模式为骨架弯曲振动和扭曲振动，C－O、C－C的扭曲振动在三个最低频率中分布占10－30％。12－冠－4在该区有18个频率，除570和547cm~(-1)处，都是二重简并的，六个最低频率的振动模式完全属于C－O、C－C键的扭曲振动，其它振动小于10％，所以200 cm~(-1)以下可称为12－冠－4的扭曲振动区，在600－200cm~(-1)之间的12个频率主要是骨架的弯曲振动，也有一定量的亚甲基wag、twist、rock振动。12－冠－4的简正坐标分析尚未有人做过。二氧六环的计算结果与Snyder和Zerbi的分析相吻合，12－冠－4和二氧六环两分子势能分布的相对一致性证明了对12－冠－4的简正坐标分析基本是正确的。本文比较了二分子的力常数和振动频率，探讨了环的大小对振动光谱的影响。四、NRCC程序简介 NRCC程序由CART、GMAT和FPERT三个程序组成，即可联一起运用，亦可分开独立进行运算。该程序功能强，所占内存大，适于大、中型计算机使用。CART程序之名字取自Cartisian Co-or-dinates的前四个字母，功能系由分子结构参数（键长、键角）计算分子内各原子的笛卡尔坐标。GMAT程序之名字取自G matrix的前四个字母，功能系由分子内各原子的笛卡尔坐标，原子质量和内坐标定义计算分子内各原子的坐标交换矩阵B和Wilson振动动能矩阵G。FPERT程序之名字取自F Perturbation的前五个字母，功能系由分子振动功能矩阵G、势能常数即力常数矩阵F计算分子的简正振动频率和势能分布矩阵，再通过实验频率精化势能矩阵F。NRCC程序可对含30个原子、60个内坐标的分子进行简正坐标分析，扩充后容量增大一倍。该程序可选用一般价力场(General Valence Force Field, 简称GVFF)和UBS力场(Urey-Bradley-Shimanouchi Force Field)，简称UBSFF或UBFF)。可选用对称化U矩阵，可自行决定力场精化次数和阻尼常数以限制精化结果的收敛性。五、NRCC程序在TRS－80微型机上移植试尝（该部分曾在第三届长春夏季化学讨论会上宣读）针对NRCC程序占内存空间大、难以在微型机上实现的情况，作者将NRCC程序改编为BASIC语言，改变程序的原来结构，形成一组BASIC语言程序：CART／BAS、GMAT／BAS和VIFR／BAS，改编后的BASIC程序在TRS－80微型机调试通过，TRS－80机字长8位，New Dos系统内存32K。改写后的程序只保持了原程序的基本原理，在内存，语句上改动很大，以适于微型机使用。数据在程序中直接嵌入，利于修改替换，且BASIC语言简单易学，便于操作。CART／BAS程序可计算含30个原子以内的分子的笛卡尔坐标，GMAT／BAS程序可计算含20个原子、45个内坐标的分子的G矩阵，VIFR／BAS程序可计算含15个原子的分子的简正振动频率。利用这组程序，作者以二氧六环分子为例做了一些试尝运算，误差14.4 cm~(-1)，相对误差1.8%，结果较理想。

Exciton states in isolated quantum wires

The exciton states in isolated and semi-isolated quantum wires are studied. It is found that the image charges have a large effect on the effective Coulomb potential in wires. For the isolated wire the effective potential approaches the Coulomb potential in vacuum at large z distance. For the semi-isolated wire the effective potential is intermediate between the Coulomb potential in vacuum and the screened Coulomb potential at large distance. The exciton binding energy in the isolated wire is about ten times larger than that in the quantum well, and that in the semi-isolated wire is also intermediate between those in the isolated wire and in the quantum well. When the lateral width increases the binding energy decreases further, and approaches that in the quantum well. The real valence-band structure is taken into account, the exciton wave functions of the ground state in the zero-order approximation are given, and the reduced mass is calculated. The effect of the coupling between the ground and excited states are considered by the degenerate perturbation method, and it is found the coupling effect is small compared to the binding energy.

Photoluminescence of GaInP under high pressure

Photoluminescence of GaInP under hydrostatic pressure is investigated. The Gamma valley of disordered GaInP shifts sublinearly upwards with respect to the top of the valence band with increasing pressure and this sublinearity is caused by the nonlinear relationship between lattice constant and hydrostatic pressure. The Gamma valleys of ordered GaInP rise more slowly than that of the disordered one and the relationship between the band gap and the pressure can not be explained in the same way. Taking into account the interactions between the Gamma valley and the folded L valleys, as well as, the X valleys, the experimental pressure dependences of the band gap of ordered GaInP epilayers are calculated and fitted quite well using first order perturbation theory. The results indicate that simultaneous ordering along [111] and [100] directions can occur in ordered GaInP. (C) 1996 American Institute of Physics.

A DOUBLE-QUANTUM-WELL IN A DRIVING LASER FIELD

The dynamic effect of electrons in a double quantum well under the influence of a monochromatic driving laser field is investigated. Closed-form solutions for the quasienergy and Floquet states are obtained with the help of SU(2) symmetry. For the case of weak interlevel coupling, explicit expressions of the quasienergy are presented by the use of perturbation theory, from which it is found that as long as the photon energy is not close to the tunnel splitting, the electron will be confined in an initially occupied eigenstate of the undriven system during the whole evolution process. Otherwise, it will transit between the lowest two levels in an oscillatory behavior.

Strain effects on optical polarisation properties in (11(2)over-bar2) plane GaN films

We present the theoretical results of the electronic band structure of wurtzite GaN films under biaxial strains in the (11 (2) over bar2)-plane The calculations are performed by the kappa p perturbation theory approach through using the effective-mass Hamiltonian for an arbitrary direction The results show that the transition energies decrease with the biaxial strains changing from -0 5% to 0 5% For films of (11 (2) over bar2)-plane, the strains are expected to be anisotropic in the growth plane Such anisotropic strains give rise to valence band mixing which results in dramatic change in optical polarisation property The strain can also result in optical polarisation switching phenomena Finally, we discuss the applications of these properties to the (11 (2) over bar2) plane GaN based light emitting diode and lase diode

数值摄动算法及其CFD格式

数值摄动算法将流体动力学效应耦合进NS方程组和对流扩散(CD)方程离散的数学基本格式(MBS),特别是耦合进最简单的一阶迎风和二阶中心格式之中,由此构建成一系列新的摄动格式(PS).构建PS的主要步骤是将MBS中的通量重构为步长的幂级数,利用空间分裂和导出的高阶流体动力学线性关系式,并引入下游不影响上游的对流运动规律,通过消除重构格式修正微分方程的截断误差诸项求出幂级数的待定系数,由此获得非线性PS.PS的项是MBS中对应项与R△x(及λR△x)之简单多项式的乘积,R△x和λ分别是网格Reynolds数和网格CFL数.PS和MBS使用相同结点,简单性彼此相当,但PS精度高,稳定范围大,例如PS包含了许多绝对稳定高阶迎风和中心有限差分(FD)格式和绝对正型有限体积(FV)格式,这些格式对网格Reynolds数的任意值均为不振荡格式.数值摄动算法因此是构建高精度不振荡CFD格式的新方法.PS用于计算不可压缩流,可压缩流,液滴萃取传质,微通道两相流等,均获得良好数值结果或与已有Benchmark解一致的数值结果.已有文献称数值摄动算法为新型高精度方法和高算法,文中也讨论了一些值得进一步研究的课题

对流扩散方程的三阶迎风格式的数值摄动高精度重构

利用高智提出的数值摄动算法,把求解对流扩散方程常用三阶迎风格式(3-UDS)(粘性项和对流项分别用二阶中心格式和3-UDS离散)进行了高精度重构,包括使用离散单元内所有节点的全域重构和分别使用上下游节点的上下游重构,得到两类新的更高阶精度迎风差分格式,称为高的迎风差分格式(记作GUDS)。讨论了GUDS的数学性质,GUDS比原来的3-UDS精度显著提高;全域重构的GUDS和3-UDS均为条件稳定,一些上下游重构GUDS为绝对稳定。本文通过稳定性分析和四个算例(一维常系数、变系数、非线性及二维变系数对流扩散方程)的计算证实了GUDS的优良性质。上下游重构GUDS为避免在3-UDS中使用人工粘性提供了一条有效途径,适合于求解高Reynolds数线性和非线性问题。

Initiation and development of water film by seepage

When water seeps upwards through a saturated soil layer, the soil layer may become instability and water films occur and develop. Water film serves as a natural sliding surface because of its very small friction. Accordingly, debris flow may happen. To investigate this phenomenon, a pseudo-three-phase media is presented first. Then discontinuity method is used to analyze the expansion velocity of water film. Finally, perturbation method is used to analyze the case that a water flow is forced to seep upwards through the soil layer while the movement of the skeleton may be neglected relative to that of water. The theoretical evolutions of pore pressure gradient, effective stress, water velocity, the porosity and the eroded fine grains are obtained. It can be seen clearly that with the erosion and re-deposited of fine grains, permeability at some positions in the soil layer becomes smaller and smaller and, the pore pressure gradient becomes bigger and bigger, while the effective stress becomes smaller and smaller. When the effective stress equals zero, e.f. liquefaction, the water film occurs. It is shown also that once a water film occurs, it will be expanded in a speed of (U)(t)/(1 - E >).

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mecha nism of destabilization is studied for the rotating vortices (scroll waves and spiral waves) in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional (2D) system undergoes asynchronized drift along a straightline, and a 3D scrolling with its filament closed into a circle can be reoriented only if the direction of wavenumber of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scrollring, the approximate formulas are given to exhibit qualitative agreements with the observed results.

Delta-resonance effective mass in medium

Based on the relativistic chiral effective field theory, we study the effective mass of the Delta-resonance in medium by investigating the self-energy of the Delta-resonance related to the pi N decay channel in symmetric nuclear matter. We find that the effective mass of Delta-resonance decreases evidently with increasing nuclear density rho. In our calculation, we also consider the influence of the shifts of the nucleon mass, pion mass and its decay constant due to the restoration of chiral symmetry in medium. The results are roughly consistent with the data given by Lawrence Berkeley National Laboratory.

Gravitational corrections to energy-levels of a hydrogen atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky-Moriya interactions

We investigate solitary excitations in a model of a one-dimensional antiferromagnet including a single-ion anisotropy and a Dzyaloshinsky-Moriya antisymmetric exchange interaction term. We employ the Holstein-Primakoff transformation, the coherent state ansatz and the time variational principle. We obtain two partial differential equations of motion by using the method of multiple scales and applying perturbation theory. By so doing, we show that the motion of the coherent amplitude must satisfy the nonlinear Schrodinger equation. We give the single-soliton solution.

Study of the capacitance coupling in accelerators

The relation between the input impedance and the characteristic parameters of a cavity, such as the resonance frequency, shunt impedance and. the quality factor, has been obtained based on the equivalent circuit of the cavity and the coupling system. Using the matching condition, the ratio of coupling capacitance to the equivalent capacitance of the cavity can be acquired as a function of the characteristic parameters of the cavity, the value of the coupling capacitance can be obtained with a help of a numerical simulation and the perturbation theory, and then the perfect matching between the cavity and the transmission line can be procured. The application of these results on a model cavity is presented too.