A unified treatment of the lattice Green function,generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice

Using multinomial expansion theorems, a unified approximation for the lattice Green function, generalized Watson integral and associated logarithmic integral for the d-dimensional hypercubic lattice is presented. The validity of this approximation is tested by other calculation methods. The approximate formulas derived are satisfactory to all other approximations and are a most suitable solution for the study of related physical properties of solids. Some examples of the effectiveness of this methodology are presented.     

Magnetization curves of a spin-one Bethe lattice

An exact calculation of the spontaneous magnetization of a spin-one Ising model with the inclusion of biquadratic exchange and single ion anisotropy on the Bethe lattice is presented. The magnetization curves exhibit some unusual features as the relative strength of the single ion anisotropy is varied.     

The hadronic spectrum with dynamical fermions

Results are presented of a numerical calculation of the hadronic spectrum on a 12³×24 lattice, which incorporates the effects due to virtual quark-antiquark pairs.     

High dose implantations of antimony for buried layer applicationsrrr

A computer simulation of low energy implantation is presented. The method of calculation takes into account the inelastic processes and vacancies in the crystal lattice.

The described simulation was used for a nitrogen implanted molybdenum single crystal. From the result of the calculation the possible positions of implanted nitrogen on the surface and in the bulk were obtained. The results of simulations are compared with those measured by SIMS and AES.     

3-d Model for strain ordering in steel: I Static effects

We present a spring-defect model in 3-dimensions to describe the connection between elastic distortion and interstitial carbon ordering associated with phase transition from a body centred cubic (BCC) to body centered tetragonal (BCT) structure in BCC metals such as α-iron. The presence or the absence of the carbon is modelled in terms of a pseudo spinŝ=+1or -l.An Ising interaction between carbon atoms is recovered after eliminating the lattice degrees of freedom, which is longranged. The coupling between the spin and lattice degrees of freedom allows for a systematic study of ferroelasticity and the variation of the lattice parameter with carbon concentration. The mean field results for the paraelastic to ferroelastic transition, lattice parameter and static compliance are presented. The significant feature of this calculation is not only a derivation of the defect-defect interaction, but also an explicit calculation of the strain dipole tensor associated with each defect, from a microscopic model.     

Enhancement of the LABSWE for shallow water flows

In the lattice Boltzmann method for the shallow water equations (LABSWE), the force term involves the first order derivative related to a bed slope, which has to be determined using the centred scheme for an accurate solution. However, such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice Boltzmann method. This paper shows how to remove this drawback from the LABSWE by incorporating the bed level into the lattice Boltzmann equation in a consistent manner with the lattice Boltzmann approach. Three numerical tests have been presented to verify the proposed method.     

Response-function theory of laser-stimulated desorption of atoms from solid surfaces

Laser-stimulated desorption fiom solid surfaces is studied as a special case of the theory of linear response functions. For many problems, for example calculation of the minimum intensity of the laser radiation field necessary for desorption, it is shown that the only dynamical property of the host system (lattice) which is required is the Laplace transform of the “response function” of the atom of the host lattice to which the adsorbed atom is attached. The results for one-dimensional host lattices with N atoms are compared with similar results obtained recently, using a quite different approach, by Murphy and George, Surface Sci. 102 (1981) L46. Effects of dimensionality of the host lattice are discussed, and an explicit comparison is presented of the results for simplified one- and three-dimensional host lattice models. Applications of the work to calculation of frequencies of normal modes of the adsorbed systems which are localized at the adsorbates (“localized modes”) are discussed and compared with previous analyses.     

The sixth frequency moment of the relaxation-shape function for a Heisenberg paramagnet

A correction to the hitherto published expression for the sixth frequency moment of the relaxation-shape function of a Heisenberg paramagnet at elevated temperatures is presented. The results are in accord with a computer calculation for a face-centred cubic lattice with nearest- neighbour exchange interactions.     

Variational Calculation of Lattice SU(N)/ZN Gauge Systems for N = 3~6

A variational calculation scheme of SU(N)/Z_N lattice gauge models for large but finite N is presented. The order parameter, the internal energy (E), and the phase transition points of lattice SU(N)/Z_N gauge systems for N = 3~6 are calculated. The results of (E) are in good agreement with Monte Carlo simulations.     

A theorem concerning twisted and untwisted partition functions in and lattice gauge theories

In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes.     

Lattice calculation of the lowest-order hadronic contribution to the muon anomalous magnetic moment

We present a quenched lattice calculation of the lowest order [O(alpha(2))] hadronic contribution to the anomalous magnetic moment of the muon which arises from the hadronic vacuum polarization. A general method is presented for computing entirely in Euclidean space, obviating the need for the usual dispersive treatment which relies on experimental data for e(+)e(-) annihilation to hadrons. While the result is not yet of comparable precision to those state-of-the-art calculations, systematic improvement of the quenched lattice computation to this level is straightforward and well within the reach of present computers. Including the effects of dynamical quarks is conceptually trivial; the computer resources required are not.     

Ab initio study of pressure-induced magnetic transition in manganese pnictides

We report a density functional calculation on the NiAs-type Mn-based pnictides. The total energy as a function of volume is obtained by means of self-consistent tight-binding linear muffin–tin orbital method by performing spin and non-spin polarized calculation. From the present study, we predict a magnetic-phase transition from ferromagnetic (FM) to non-magnetic (NM) around 49 and 35.7 GPa for MnAs and MnSb, respectively. The pressure-induced transition is found to be a second-order transition. The band structure and density of states (DOS) are plotted for FM and NM states. Apart from this the ground-state properties like magnetic moment, lattice parameter and bulk modulus are calculated and are compared with the available results. Under large volume expansion these compounds exist in zinc-blende (ZB) structure, which shows half metallicity. The magnetic moment and equilibrium lattice constants for ZB structure are obtained as well as band structure and DOS are presented.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

Localized vibrations of point defects in body-centred cubic lattices

The paper gives an exact calculation of the localized frequencies of substitutional defects in a body-centred cubic lattice by the method of Green's functions and compares it with the approximate calculation carried out after [14]. The exact calculation is based on newly computed Green's functions of a b.c.c. lattice [18]. It is shown how by means of group theory the symmetry of the system can be used both in an approximate and in the exact calculation. Some symmetry relations between Green's functions, which limit the number of functions necessary for numerical calculations, are derived.     

A form factor model for exclusive B- and D-decays

An explicit model is presented which gives the momentum transfer-dependent ratios of form factors of hadronic currents. For the unknown Isgur-Wise function and its generalization for transitions to light particles a simple phenomenological Ansatz is added. The model allows a calculation of all form factors in terms of mass parameters only. It is tested by comparison with experimental data, QCD sum rules and lattice calculations.     

皮秒激光烧蚀Al膜的理论分析与实验验证

为研究Al膜受短脉冲激光作用时的能量传输过程,建立了一维半经典双温热传导模型。根据材料加工过程的熔化现象,对模型的相变区域进行有效设置。通过有限元法求解,得到晶格温度随时间分布的规律。根据自由电子气理论优化了模型,得到Al膜表面反射率和热吸收系数随时间的分布图。得到了激光辐照所产生热电场的分布规律,并分析了电子温度梯度对其影响。描绘出电子漂移运动速度的分布规律,证实激光作用产生的热电场是电子漂移运动的主导因素,发现最大漂移速度位置随时间的延长而加深。对激光作用后的晶格温度进行了区域性分析,定义了过热加热区,并得到激光烧蚀深度随时间的变化关系。实验结果表明,不同功率皮秒激光烧蚀Al膜的深度接近于理论计算结果。     

Deformation charge distribution and total energy for perowskites

A microscopic theory of solids is presented which allows the calculation of lattice properties from first principles. The method is based on the Density-Functional-Theory and a new version of the Linear-Muffin-Tin-Orbital method, which includes nonspherical charge distributions in the total energy calculations. Explicit results for BaTiO₃ and SrTiO₃ are reported. The deformations of the charge density due to a homogeneous volume change and due to a soft mode deformation were determined. Differences between BaTiO and SrTiO₃ and the nature of the chemical bonding are discussed. Calculated cohesive energies and lattice constants agree well with experimental data.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday     

Dynamic Properties of Proton Transfer in the Anharmonic-Interaction Hydrogen Bond Systems

We analyze the properties of the excited solitary-wave model in the case of anharmonic-interaction of heavy ionic lattice in hydrogen bond systems.in this case,some new phenomena appear,We find different types of solutions for the proton displacement and influences on the kinks and pulse solitary waves by numerical calculation.For each of them we have presented a direct relation with the effective potential of the system.     

Fermionic Representation of Two-Dimensional Dimer Models

Dimer models in two dimensions give rise to well-known statistical lattice problems, which can be exactly solved by the same combinatorial techniques associated with the Ising model and which have been used to account for the phase transitions in a number of physically interesting systems. More recently, dimer models have been regarded as classical limits of the quantum ground state of some antiferromagnetic systems. We then revisit an early transfer-matrix calculation for the dimer model on the simple square lattice. We write a spin representation for the transfer matrix associated with the canonical partition function of two paradigmatic dimers models, on the 4–8 lattice, with an Ising-type transition, and on the brick lattice, with a peculiar commensurate–incommensurate transition. Using standard techniques, the problem is reduced to the calculation of the eigenvalues of a system of free fermions.