The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Exchange-correlation energy in the subbands of silicon doping superlattices

The energy subbands in three types (pn⁺p, pnpn, nipi) of Si and GaAs doping superlattices are calculated self-consistently including the exchange-correlation energy given by the density functional method. The results show that the exchange-correlation term is more important in Si than in GaAs in all three cases. For the same doping levels, layer thicknesses and electron concentrations, the shift in the lowest subband energy from the value given by the Hartree Approximation is 20–50% greater in Si than in GaAs.     

THE DIELECTRIC FUNCTION OF AN ELECTRON SYSTEM IN A PERIODIC STRUCTURE: VAA THEORY+

A general expression for the dielectric function of an electron system in a period structure has been derived by using linear response theory with the assumption that the equilibrium electronic density differs slight1y from its average value. Starting from the BBGKY equations,the theory is formulated in the Velocity Average Approximation.Numerical results for the dispersion and damping of plasmons and for the longitudinal dielectric function are given in the case of sinusoidally modulated structures.     

The effect of the topography of heterogeneous surfaces on the adsorption energy distribution,evaluated by the asymptotically correct,condensation approximation

In our previous paper [1], we used the well-known CA(Condensation Approximation) method, to evaluate the adsorption energy distribution from experimental isotherms, assuming that adsorption sites of different adsorption energies are distributed on adsorbent surface completely at randon.This note is an extension of our theory, using the ACCA, (Asymptotically Correct Condensation Approximation), which, in the hitherto investigation, was used only to adsorption on surfaces, with the patchwise topographical distribution of adsorption sites.     

Local magnetic moment calculation in random Cu-Ni and Fe-Cr alloys

A simple method to calculate the local magnetic moments in random binary alloys has been developed within the Coherent Potential Approximation. Such a method has been applied to the case of Cu-Ni and Cr-Fe ferromagnetic alloys. The results have been compared with the experimental data obtained from neutron scattering experiments.     

A non-crossing approximation for the study of intersite correlations

We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a self-consistently embedded periodic cluster of size . It is a fully causal and systematic approximation to the full lattice problem, with corrections in two dimensions. The NCA we develop is a systematic approximation with corrections . The method will be discussed in detail and results for the one-particle properties of the Hubbard model are shown. Near half filling, the spectra display pronounced features including a pseudogap and non-Fermi-liquid behavior due to short-ranged antiferromagnetic correlations. Received 16 June 1999     

Modelling diffraction by facetted particles

A method to approximate azimuthally resolved light scattering patterns and phase functions due to diffraction and external reflection by strongly absorbing facetted particles is demonstrated for a cube and compared with results from an exact method, T-matrix. A phase function averaged over a range of orientations of a strongly absorbing hexagonal column of aspect ratio unity has been calculated and tested against Discrete Dipole Approximation (DDA) results for a size parameter of 50.     

Tunability response in exponentially graded ferroelectrics: A TIM model approach

Relative dielectric function response associate to a non-homogeneous layered ferroelectric system is calculated in the framework of the Mean Field Approximation (MFA) for the Transverse Ising Model (TIM). Analytical self-consistent expressions for the average polarization, dielectric susceptibility, and tunability percentage are outlined and solved for different configurations and sizes. It is found that exponentially graded ferroelectrics magnify the tunability response for stronger interlayer coupling and it reaches its saturation value for smaller intensities of the applied electric field.     

10Neq+(q=1～3)的电荷损失截面

采用托马斯－费米近似和二体碰撞近似,计算了多电荷离子１０Ｎｅ＾ｑ＋与中性原子Ｈ和Ｈｅ碰撞的电荷损失截面以及电子的动量分布和离子势函数分布。     

Extraction of the spurious states from the solution of the motion equation within the random phase approximation

The general form of nuclear Hamiltonian equation of motion is derived within the Random Phase Approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the equations of motion is shown. The general method of extraction of spurious states from the solution of the RPA equations of motion is proposed.     

Extension of the Random-Phase Approximation for <Emphasis Type="Italic">γ</Emphasis>-soft nuclei

The variational method is formulated which extends the Random-Phase Approximation to γ-soft nuclei.     

The spin wave stiffness constant in itinerant electron ferromagnetic transition metal dilute alloys

The spin wave stiffness constant is calculated for itenerant electron ferromagnetic transition metal dilute alloys. Calculations are made in the Random Phase Approximation, using the method of effective magnon Hamiltonian. The term in the magnon energy proportional to impurity concentration is calculated by summing up exactly a perturbational series.     

分子动力学模拟纳米晶体银的结构和性能

通过分子动力学方法,采用以局域密度（ＬＤＡ）氨似和二阶动量矩（ＳＭＡ）近似为基础的多体热函数,模拟了纳米面心立方晶体银的结构,对模拟的结果进了不同尺寸的纳米晶体的能量分布,弹性表面能及熔点等计算,并与相应的实验结果进行了比较,结果表明采用此多体势函数模拟纳米晶体的结构和性能,比用其它势函数更精确,与实验结果更吻合。     

The calculation of chemical shifts in conjugated molecules

Within the context of pi-electron theory an expression for the proton chemical shifts in conjugated molecules is derived via a current density approach. Using London integral approximations the method is applied to benzene and naphthalene. Provided a particular form of the London Approximation is used, theoretical values in good agreement with experiment are obtained.     

Generalized Quasi-Chemical Approximation for a lattice gas: Application to CO on RU

The interaction between adsorbed particles is treated in a generalized Quasi-Chemical Approximation, which allows to take into account larger groups of sites.It turns out that for CO on RU it is sufficient to consider groups of three sites, whereas the Quasi-Chemical Approximation with only two sites in a group is insufficient. Good agreement with experimental results for the desorption rate of CO on RU has been obtained.     

A monotone finite volume method for advection–diffusion equations on unstructured polygonal meshes

We present a new second-order accurate monotone finite volume (FV) method for the steady-state advection–diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes and guarantees solution non-negativity. The interpolation-free approximation of the diffusive flux uses the nonlinear two-point stencil proposed in Lipnikov [23]. Approximation of the advective flux is based on the second-order upwind method with a specially designed minimal nonlinear correction. The second-order convergence rate and monotonicity are verified with numerical experiments.     

Role of polarization interaction in photoionization of negative ions of alkali metals

Photoionization processes of negative ions of sodium, potassium, and rubidium were investigated. Calculations of the dependence of the photoionization cross section on the photon energy were performed within the Random Phase Approximation with Exchange for outer subshells (RPAE) and within the Generalized Random Phase Approximation with Exchange (GRPAE) for inner subshells. The latter theoretical approach includes both many-electron correlations and core rearrangement due to escape of one of the electrons from the system. The results of calculations for the negative sodium ion were found to be in good agreement with experimental data. Better agreement was achieved by allowing dynamical polarization of the electron core. It manifests itself as a many-electron response to variation of the external electromagnetic field, which results from the excitation of the many-electron system. Detailed study of the main mechanisms determining the cross section dependence profile was carried out. These mechanisms are the inter- and intrachannel correlations acting as a many-electron response to the external field, the electron core rearrangement, and the dynamic polarization. Besides sodium and potassium ions, photoionization of rubidium ion was investigated. A new method accounting for polarization corrections to optical transition amplitudes based on combination of the Dyson equation and RPAE is proposed.