Modified Perturbation Theory of an Anharmonic Oscillator

A modification of the perturbation theory of a symmetrical anharmonic oscillator is suggested. A more complex zero-order approximation of perturbation theory that considers to a certain degree anharmonicities is chosen rather than a harmonic oscillator model. This approximation is an analog of the self-consistent field model well known in the theory of many-particle systems. A comparison of modified and conventional perturbation theories demonstrates that the modified perturbation theory has much wider applicability range. It can be used for larger values of the parameters at which the conventional perturbation theory becomes inapplicable, namely, for strong anharmonicity and upper energy levels.     

Anharmonic properties of rocksalt structure solids

An effort has been made for obtaining the anharmonic properties of rocksalt structure solids starting from primary physical parameters viz. nearest-neighbor distance and hardness parameter assuming long- and short-range potentials at elevated temperatures. The elastic energy density for a deformed crystal can be expanded as power series of strains for obtaining coefficients of quadratic, cubic and quartic terms which are known as the second-, third- and fourth-order elastic constants, respectively. When the values of the higher-order elastic constants are known for a crystal, many of the anharmonic properties of the crystal can be treated within the limit of the continuum approximation in a quantitative manner. In this study, higher-order elastic constants are computed up to their melting temperature for rocksalt structure solids, which are alkali cyanides, sodium and potassium halides. The first order pressure derivatives of second- and third-order elastic constants, the second-order pressure derivatives of second-order elastic constants and partial contractions are also evaluated at different temperatures for these substances. The results thus obtained are compared with experimental data and found in well agreement with present values.     

Anharmonic oscillators in higher dimension: Accurate energy eigenvalues and matrix elements

Energy eigenvalues and matrix elements of various anharmonic oscillators are determined to a high accuracy by applying a method for determining the eigenvalues and eigenvectors of real symmetric para-p diagonal matrices (described in the preceding paper). Our results for the 2- and 3-dimensional oscillators are new and complement similar accurate results for the one dimensional oscillators available in the literature.     

Anharmonic excitations in the FPU and FK models

The properties of vibrational localized (breathers) and traveling (anharmonic phonons) waves are discussed in an infinite, one-dimensional, monoatomic crystal for the Fermi-Pasta-Ulam and Frenkel-Kontorova models. The shooting and finite difference schemes have been implemented to reckon the displacement fields of breathers and anharmonic phonons, respectively. These tools provide localized and traveling waves proving to be indefinitely stable in simulations carried out by solving the equations of motion. The emphasis is laid on the role of the cubic and quartic terms of the anharmonic potential which turn out to oppose and to shore up the restoring force, respectively. The case of vibrational modes arising in an anharmonic crystal subject to a soft phonon induced instability is also addressed. Received 7 November 2001 and Received in final form 5 February 2002 Published online 6 June 2002     

Anharmonic spectra of methanol and silanol: A comparative study

Anharmonic vibrational spectra of methanol and silanol as well as of some of their deuterated isotopomers are analysed using the vibrational self-consistent field approximation corrected by second order perturbation theory (cc-VSCF). Experimental frequencies in the case of methanol and its isotopomers are in general reproduced and anharmonic effects in their vibrational spectra are suitably explained. The similar species containing Si, i.e., silanol, is very unstable. Experimental data about its vibrational spectra are rare in the literature and the only theoretical data available come from the harmonic approach. Thus, to predict further anharmonic effects in its vibrational spectra, we extend our results on methanol to the silanol molecule.     

六次非简谐振子的多尺度微扰理论

应用多尺度微扰理论, 对于弱耦合常数的六次非简谐振子得到了其运动方程的经典和量子情况下的一阶解. 与Taylor级数解不同的是, 无论是在经典和量子解中频率移动出现在各阶表达式中, 因此多尺度微扰理论是优于Taylor级数解的一种处理弱耦合常数非简谐振动的近似方法.     

广义非简谐振子的多尺度微扰理论

应用多尺度微扰理论到广义非简谐振子, 得到了一阶经典和量子微扰解. 特别是 我们的量子解在极限条件下能方便地转变为经典解, 并且坐标和动量算符的对易 关系的简化十分自然. 与Taylor级数解相比较, 无论是在经典还是在量子解 中频率移动都出现在各阶振动表达式中, 所以多尺度微扰解是弱耦合非简谐振动的较好解法.     

Anharmonic Vibrational Signatures of DNA Bases and Watson-Crick Base Pairs

在密度泛函理论水平上研究了从DNA碱基单体到Watson-Crick碱基对的结构、电荷分布、以及非谐性振动参数的变化. 通过研究参与碱基对中多重氢键的NH₂、N-H和C=O的伸缩振动模式,预测了这些模式的对角非谐性常数、非对角非谐性常数、以及非谐性振动耦合对碱基结构变化的敏感性. 研究结果揭示了DNA碱基中非谐性振动势、分子间氢键和静电相互作用之间的内在联系.     

Anharmonic dynamical behaviour in bcc zirconium

We present inelastic neutron scattering measurements of the low energy and strongly damped phonons in the high temperature bcc phase of zirconium. These phonons were investigated at different scattering vectors but equivalent phonon wave vectors in different Brillouin zones or along different but equivalent paths in the same Brillouin zone. Neither the observed differences in intensity nor in line shapes can be explained by the coherent one-phonon scattering law . This leads to an apparent violation of the fundamental symmetry of lattice dynamics. Taking into account the strong anharmonicity of these phonons, interferences between one- and multi-phonon scattering are held responsible for these effects. Measurements in different scattering planes reveal that due to the symmetry of the bcc lattice, these effects can only be observed in certain directions. Received: 24 December 1997 / Received in final form: 9 March 1998 / Accepted: 19 March 1998     

Propagation of a Rectangular Pulse in an Anomalous Dispersive Medium

The pulse with a rectangular envelop propagating through the caesium vapour with two gain lines used inthe Wang, Kuzmich, and Dogariu [Nature (London) 406 (2000) 277] experiment is studied. It is shown that there existsan obvious distortion for the pulse.     

Computer Simulation Study of Thermal Conduction in 1D Chains of Anharmonic Oscillators

In this work thermal conduction in one-dimensional(1D) chains of anharmonic oscillators are studied using computer simulation.The temperature profile,heat flux and thermal conductivity are investigated for chain length N = 100,200,400,800 and 1600.In the computer simulation anharmonicity is introduced due to Fermi-Pasta-Ulam-β(FPU-β) model.For substrate interaction,an onsite potential due to Frenkel-Kontorova(FK) model has been used.Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N.For the thermal conductivity K,KN to N obey the linear relation of the type KN = 0.8805N.It is shown that thermal transport is dependent on phonon-phonon interaction as well as phonon-lattice interaction.The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ = 0.133 + 0.804β.It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.     

Propagation of a Rectangular Pulse in an Anomalous Dispersive Medium

The pulse with a rectangular envelop propagating through the caesium vapour with two gain lines used in the Wang, Kuzmich, and Dogariu [Nature (London) 406 (2000) 277] experiment is studied. It is shown that there exists an obvious distortion for the pulse.     

用从头算方法研究GeCl2分子的非谐振力场和光谱常数

用从头算方法的MP2和CCSD（T）方法结合cc-pVTZ基组计算了二氯化锗同位素（⁷⁰GeCl₂、⁷²GeCl₂和⁷⁶GeCl₂）分子的平衡结构、光谱常数和非谐振力场.二氯化锗的几何结构、转动常数、振转相互作用常数、谐频、非谐振常数、四次和六次离心畸变常数、三次和四次力常数的计算结果与实验结果符合较好,二氯化锗分子的同位素效应较小,可能的原因是Ge同位素的质量变化相对较小.两种方法计算的结果均与实验结果符合,但CCSD（T）方法比MP2计算结果的偏差稍大一些,可能的原因是CCSD（T）方法在描述过共价Cl原子的电子相关时不够充分.     

聚合物电光波导传播常数和损耗系数的微扰解

对于聚合物电光波导,依据理想光波导耦合理论的微扰理论,推导传播常数和损耗系数的近似表达式,从而将求解本征值的复杂复数运算简化成简单实数运算。数值计算表明,这些近似解与正确解很好相符。给出的近似公式和特征曲线可供聚合物电光波导及其器件的设计和制备作参考。     

光脉冲通过含有色散与增益型缺陷的一维光子晶体的传播

研究了光脉冲通过含有色散和增益型缺陷的一维光子晶体的传播行为.缺陷的色散与增益性质用Lorentz振子模型描述.随着振子强度的变化，脉冲峰的传播呈现极慢光速和超光速的传播行为，但能量速度小于真空中的光速c.脉冲峰的超前与落后是各Fourier分量在介质中获得了不同的相移和幅度改变后重新相干叠加的结果. 关键词： 光子晶体 缺陷 光脉冲传播 能量速度     

双曲余弦高斯光束通过有光阑限制的ABCD光学系统的传输

对双曲余弦高斯光束通过有硬边光阑的一阶ABCD光学系统的传输进行了研究,采用将矩形域函数表示为复高斯函数叠加的技巧,推导出了解析的传输公式,在特殊情况下,该公式简化为在无光阑情况下的传输公式,对双曲余弦高斯光束通过有光阑限制的薄膜镜聚焦进行了数值计算,计算结果与直接由柯林斯（Collins)公式所得结果一致,且此解析方法便于进行物理分析,可节约大量机时。     

基于非谐力场的HOI分子振动光谱研究

应用包含非迭代三激发(CCSD(T))、迭代三激发(CC3)及其变体(CCSDT-3)的耦合簇理论(CC)和密度泛函理论(DFT)之B3LYP方法,使用直到五阶的自洽相关一致基组aug-cc-pVxZ/aug-cc-pVxZ-PP(x=T, Q, 5),首先优化出HOI的平衡结构,接着在该结构附近采样势能点并将其在简正坐标下拟合成直到四阶的多项式力场,依据该力场结合振动自洽场(VSCF)、振动组态相互作用(VCI)和二阶振动微扰理论(VPT2)进行非谐振动分析,精确预期了HOI的基频、直到v₁+v₂+v₃=3的和频与倍频,得到其转动常数、旋振相互作用常数、非谐性常数和离心畸变常数,同时振子强度被估计,氘取代效应被进一步考察。结果表明：当前计算值与已知实验结果符合良好,其中耦合簇理论计算的振动光谱常数更加可靠,DFT误差明显偏大,但两者计算的振动频率却相当一致;并非基组越大,计算得到的非谐振动常数/频率与实验更符合,总体来讲CC3和CCSDT-3的结果更值得信赖;HOI/DOI都没有共振发生。     

在梯形四能级原子系统中的慢光和超光速传播

研究了梯形四能级冷原子系统的非线性光学行为,在一微波场耦合两上简并能级时双暗态共振将会出现。在合适的参数条件下,系统将表现出正常色散与反常色散之间的转变。改变耦合场和微波场的大小能够调控慢光和超光速间的转变。     

渐变折射率波导传播特性微扰计算的代数递推公式

应用量子力学的超位力定理（HVT）和赫尔曼－费恩曼（Hellmann-Feynman）定理（HFT），导出了用微扰法计算渐变折射率平面波导传播常数各级近似值的代数递推公式，并给出了由传播常数近似值计算模场近似表达式的代数式。计算了几个典型实例，此法的特点是便于直接计算任意级近似的传播常数及模场分布，且可推广到二维波导的计算。     

双偏心椭圆高斯光束在一阶ABCD光学系统中的传输特性

通过求解时谐条件下的亥姆霍兹方程,得到一个特解双偏心椭圆高斯光束,该光束由两个偏心椭圆高斯光束叠加而形成的,可用于描述大功率激光二极管远场分布双峰特性.分析了该光束的光场模型,运用惠更斯-菲涅尔广义积分公式,得到了该光束在一阶ABCD光学系统中的传输场分布和解析表达式,在此理论基础上,数值计算得到光场分布和远场发散角,并运用该光束模型模拟了新型激光二极管光场分布,理论结果与实际结果吻合.