A JWKB analysis of the sextic anharmonic oscillator in d dimensions

On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional sextic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. The predicted results are in good agreement with known numerical values.     

First principles study of structural and electronic properties of different phases of boron nitride

A theoretical study of structural and electronic properties of the four phases of BN (zincblende, wurtzite, hexagonal and rhombohedral) is presented. The calculations are done by full potential (linear) augmented plane wave plus local orbitals (APW+lo) method based on the density functional theory (DFT) as employed in WIEN2k code. Using the local density approximation (LDA) and generalized gradient approximation (GGA-PBE) for the exchange correlation energy functional, we have calculated lattice parameters, bulk modulus, its pressure derivative and cohesive energy. In order to calculate electronic band structure, another form of the generalized gradient approximation proposed by Engel and Vosko (GGA-EV) has been employed along with LDA and GGA-PBE. It is found that all the three approximations exhibit similar band structure qualitatively. However, GGA-EV gives energy band gap values closer to the measured data. Our results for structural and electronic properties are compared with the experimental and other theoretical results wherever these are available.     

Free-Space Propagation of the Generalized Radiance Defined in Terms of the Coherent-Mode Representation of Cross-Spectral Density Function

The equation for free-space propagation of the generalized radiance defined formerly by the authors in terms of the coherent-mode representation of the cross-spectral density function is derived within the accuracy of the paraxial approximation. It is shown that, in the short-wavelength limit, this generalized radiance obeys in a good approximation the fundamental radiative transfer law of classical radiometry.     

Paraxial Approximation of Modern Radiometry for Beamlike Wave Propagation

A new approach to the construction of a system of the generalized radiometric quantities expressed in terms of the cross-spectral density function of the wave field is proposed. The key distinction of this approach lies in the fact that the initial hypothesis of beamlike wave propagation allows to invoke the paraxial approximation when deducing the generalized radiant flux. Within the framework of this approach the new expressions for the generalized radiant emittance, the generalized radiant intensity and the generalized radiance are derived. All the proposed generalized radiometric characteristics represent physically measurable quantities and, hence, may be used in practical radiometry. The results obtained in this paper can be regarded as a particular case of the modern radiometry theory in paraxial approximation for beamlike wave propagation.On leave from Kiev Polytechnic Institute, Ukraine.     

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

In this paper, we analyze the generalized Camassa and Holm （CH） equation by the improved element-free Galerkin （IEFG） method. By employing the improved moving least-square （IMLS） approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.     

Non-abelian eikonal exponentiation

Recently, Gatheral [1] has generalized the well-known exponentiation properties of soft photons in QED to the case of soft gluons in QCD in the eikonal approximation. We add three things to his work. (i) We clarify the definition of the colour weight factors which appear in the exponent. (ii) We show how the eikonal approximation can be renormalized, consistently with the exponentiation. (iii) We derive a differential equation obeyed by the cross section for emission of soft gluons with given maximum total energy. We also discuss the relationship between the exponentiation theorem and expectation values of Wilson loops.     

自治广义Birkhoff系统的平衡稳定性

研究广义Birkhoff系统的平衡稳定性问题.建立了自治广义Birkhoff系统的平衡方程;给出了自治广义Birkhoff系统的一次近似方程,利用Lyapunov一次近似理论,建立了系统平衡状态稳定性的判据;构建了Lyapunov函数,利用Lyapunov直接法,建立了自治广义Birkhoff系统平衡状态稳定性的判据.给出了若干算例以说明结果的应用.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

d2,8电子体系共价效应对光谱的影响

在含过渡金属离子的半磁半导体的光学和磁学性质研究中,由于体系的共价性较强,d轨道不再是纯d轨道,而是混合轨道t2g或eg。相应地,需要引入两个共价因子Nt和Ne。建立在混合轨道上的含有共价因子的能量矩阵称为广义能量矩阵。建立了d2,8电子体系的(45×45)阶广义能量矩阵。在广义能量矩阵中,拉卡(Racah)参量A不再是相加常量,同时,d8电子体系不能简单地视为互补的d2空穴体系,因为它们的能量矩阵形式不同。Nt和Ne虽然是属于两个不同轨道的不同的共价因子,但在数值上不能有大的差别,因为考虑进共价效应后,拉卡静电参量A对能级计算有极大的影响。这意味着在通常的光谱拟合中所采用的BCΔ方案是好的近似。以上结论被应用于ZnS∶Ni2 的d-d跃迁谱,计算结果与实验符合。     

中心快度区的双轻子不变质量分布

推广先前作者采用的夸克和π的相空间分布函数的Boltzmann近似到一个完全的表示,利用快度区的温度计算出粒子密度后,在Bjorken的(1+1)维的纵向膨胀系统中研究了双轻子的产生.发现推广的近似分布函数很大地改变了预言的夸克物质形成的特征双轻子分布.     

固态二氧化碳电子结构及性能的理论研究

采用基于赝势平面波理论的第一性原理计算方法,研究了9种结构的固态二氧化碳的结构和性质.经过结构的几何优化,得到α石英稳定结构晶格常数与他人的计算值基本一致.通过对平衡态能量的分析,我们得出β方石英(cristobalite)结构是能量最低的结构.这与文献的研究结果一致.对弹性性质的计算结果表明,除了超石英(stishovite)和立方黄铁矿(cubic-pyrite)结构之外,其他的结构都是弹性稳定的.利用基于Mulliken轨道重叠布居数的共价固体本征硬度计算方法,预测了各个结构的本征硬度值.结果表明, 关键词： 第一性原理计算 固态二氧化碳 电子结构 硬度     

Generalization of the Curtis-Godson approximation to inhomogeneous scattering atmospheres

The Curtis-Godson approximation, which was initially derived to compute the transmission through clear inhomogeneous atmospheres, has been generalized to any cloudy atmosphere by means of the scaled amount distribition. For most of the realistic atmospheres, the accuracy of this generalized approximation is comparable to or even better than for the clear case.     

高压下氧化镉弹性性质、电子结构和光学性质的第一性原理研究

 运用基于密度泛函理论的平面波赝势方法（PWP）,计算研究了氧化镉NaCl结构（B1结构）和CsCl结构（B2结构）在不同压力条件下的几何结构、弹性性质、电子结构和光学性质。交换关联能分别采用广义梯度近似（GGA）和局域密度近似（LDA）。通过比较计算和实验得到的晶格常数和体模量不难发现,LDA的计算结果更符合实验值。在高压的作用下,两种结构的导带能级有向高能级移动的趋势,而价带能级有向低能级移动的趋势,因此直接带隙变大。同时,对照态密度分布图及高压下能级的移动情况,分析了CdO两种结构在高压作用下的光学性质。     

Collective excitations in semiconductor superlattices

Collective excitations in semiconductor superlattices are studied beyond tbe random-phase approximation (RPA). The Singwi, Tosi, Land and Sjölander (STLS) theory, which accounts for exchange and short-range correlations effects through an effective potential depending on the structurc factor, is generalized to the layered electron system described by the model of Visscher and Falicov. The exact numerical solution of the STLS self-consistent equations provides information about intraplane and interplane correlations. The plasmon dispersion curves are evaluated for some typical values of the coupling constant r_s of the electron system and the distance between the planes for GaAs/AlGaAs semiconductor superlattices. For comparison, the RPA and the Hubbard approximation are also considered.     

Stochastic path integral formulation of full counting statistics

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.     

First-principles study of electronic structure and elasticity of UAlx (x=1,2,3) system

A detailed theoretical study of structural, electronic, and elastic properties of cubic UAl_x (x=1,2,3) is presented employing the pseudopotential plane-wave method based on density-functional theory. The structure parameters of these three compounds have been calculated within generalized gradient approximation (GGA) and local density approximation (LDA). The calculated results were compared with the experimental data and previous research. With the GGA approximation, the elastic constants, shear modulus, Young's modulus, and Poisson's ratio of UAl_x (x=1,2,3) are derived. According to the generalized mechanical stability criteria for cubic crystals, our calculation suggested that C15 UAl₂ and L12 UAl₃ are stable substance under hydrostatic pressures, but B2 UAl might be expected as a metastable compound, which is not reported in previous literature, and future experimental confirmation is needed. Furthermore, the calculated energy band structure and density of state (DOS) are found to be in good agreement with the theoretical values. Additionally, the charge density of these compounds have also been worked out and analyzed.     

Interpretation of the processes 3He(e,e'p)2H and 3He(e,e'p)(pn) at high missing momenta

Using realistic three-body wave functions corresponding to the AV18 interaction, it is shown that the effects of the final state interaction in the exclusive processes 3He(e,e'p)2H and 3He(e,e'p)(pn), can be successfully treated in terms of a generalized eikonal approximation based upon the direct calculation of the Feynman diagrams describing the rescattering of the struck nucleon. The relevant role played by the double rescattering contribution at high values of the missing momentum is illustrated.     

Structural, electronic and optical properties of high pressure stable phases of ZnTe

We have performed full potential linear augmented plane wave calculations to investigate the pressure induced phase transition in ZnTe. Total energies of three phases (zinc-blende, cinnabar and Cmcm) are calculated using density functional theory formalism under generalized gradient approximation and Engel-Vosko generalized gradient approximation for the exchange correlation potential approximation. The pressure stability corresponding to zinc-blende, cinnabar and Cmcm phases of ZnTe are computed. We find that cinnabar phase could be formed as a metastable phase by releasing pressure from the high pressure Cmcm phase. The obtained structural, electronic and optical results are compared with previous calculations and available experimental data. Overall good agreement is found.     

A theory of vibrations of solid solutions with inclusion of the cluster effects: Non-self-consistent and self-consistent approximations

A theory of vibrational spectra of solid solutions proposed by the author has been developed, in which a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibrational spectra of a disordered linear chain in the generalized non-self-consistent approximation has demonstrated a strong dependence of the spectrum on the number n. For n = 6, the calculated spectrum is in an excellent agreement with the result of the computer experiment performed by Dean for a chain of 8000 atoms. The maximum number of impurities in the cluster to be considered depends on the magnitude of the initial damping (in real crystals, it is damping due to anharmonicity). The spectrum has also been calculated in the generalized self-consistent approximation. This calculation gives a smeared structureless curve, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This means that the generalized self-consistent approximation overestimates the weight of the incoherent scattering processes, which leads to averaging of the phases. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.     

Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation

Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman’s approximation), the Maxwell-Garnett approximation, Wiener’s bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.