The self-consistent diagram approximation for lattice systems

We apply the self-consistent diagram approximation to calculate equilibrium properties of lattice systems. The free energy of the system is represented by a diagram expansion in Mayer-like functions with averaging over states of a reference system. The latter is defined by one-particle mean potentials, which are calculated using the variational condition formulated. As an example, numerical computations for a two-dimensional lattice gas on a square lattice with attractive interaction between nearest neighbours were carried out. The critical temperature, the phase coexistence curve, the chemical potential and particle and vacancy distribution functions coincide within a few per cent with exact or with Monte Carlo data. Received 18 March 1999 and Received in final form 8 November 1999     

The Bethe approximation for lattice gauge theories

The Bethe approximation is defined for general lattice gauge theories. It amounts to solving the model on an infinite Cayley lattice of cubes. The approximation is tested on the 4-d Z₄ model, where it is shown to reproduce accurately most of the phase diagram. It also suggests which mass vanishes in the Coulomb phase.     

The lattice baryon spectrum in first order strong coupling approximation

Lattice baryon masses are calculated in first order strong coupling approximation with staggered fermions. Particular emphasis is given to the lattice quantum numbers and their relation to the continuum symmetry. Using non-local one-link fields, we found lattice baryon states which are new in first order strong coupling approximation.     

Coulomb crystals in the harmonic lattice approximation

The dynamic structure factor &Stilde;(k,omega) and the two-particle distribution function g(r,t) of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multiphonon excitation and absorption. The static radial two-particle distribution function g(r) is calculated for classical (T greater, similarPlanck's over 2piomega(p), where omega(p) is the ion plasma frequency) and quantum (T相似文献   

Alpha particle scattering in the rigid projectile approximation

We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.     

BaVS3晶格动力学研究

采用基于密度泛函理论的平面波赝势方法,在局域密度近似下采用线性响应的密度泛函微扰理论研究了具有六角结构的BaVS3化合物的品格动力学性质,得到了整个声子谱.计算得到的г点拉曼频率和实验数据进行了比较,其中E22g模、A1g模和实验测量值符合得比较好.对于E32g模,采用线性响应计算的结果与实验值差别较大.对该模应用冻结声子方法研究后认为差异主要是由于E32g模的较强的非谐性引起的.此外V原子在平面内的振动模E12g出现了虚频.虚频的出现预示着六角相的BaVS3结构的不稳定性,从而很好地解释了该材料由六角相到正交相的结构相变.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Multilayer lattice gas model in the quasichemical approximation

The multilayer lattice gas model is dealt with in the quasichemical approximation. A restriction on the atomic stacking is also introduced in the system so that an atom can occupy only a lattice site whose underlying nearest neighbor lattice sites are all occupied by atoms. The critical condensation of atoms is investigated as the substrate potential is varied. The theory is also applied to the surface roughening of the crystalline bulk.     

On rigid projectile approximation in high energy nucleus-nucleus scattering

Rigid projectile approximation in high energy nucleus-nucleus collisions is discussed. The results are demonstrated ond- elastic scattering.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.     

Stress-stress correlation functions in lattice gases beyond Boltzmann's approximation

The complete time dependence of the stress-stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods. This provides corrections, typically of 10–20%, to the usual molecular chaos calculations, where correlation functions decay exponentially. The resulting correlation function crosses over from an initial exponential decay to the long-time behavior calculated from mode coupling theory. The present theory, applied to the viscosity, accounts for a substantial part of the observed difference between the Boltzmann theory and simulations.     

Model for lattice dynamics in metals

A lattice dynamical model for cubic metals, which satisfies the internal force equilibrium condition of the lattice, is proposed. The present model combines a linearized Thomas Fermi theory for the electron-ion interaction and the axially symmetric model for the ion-ion interaction. The computed frequencies of copper and sodium are in good agreement with the experimental data.     

Diffusion in lattice Lorentz gases : Nearest scatterers approximation

The expressions for diffusion coefficients and for velocity autocorrelation functions of lattice Lorentz gases are derived both in the nearest scatterers and Boltzmann approximations. The results are obtained for linear chain, square, triangular, simple cubic, body centred cubic, face centred cubic and face centred hyper cubic lattices. The diffusion coefficients are compared with those from the effective medium approximation for the square lattice and with computer simulation results for triangular, simple cubic and body centred cubic lattices.     

Generalized bethe approximation in lattice models of long polymers

The phase transition behavior of a self-avoiding linear polymer model on a three-dimensional lattice is studied. An approximate procedure is proposed which gives the exact divergence of the specific heat aboveT _c for the two-dimensional case. In three dimensions our method predicts a finite value forC atT _c and demonstrates clearly what neglected contributions to the partition function lead to such a behavior of the model.     

The mean-field approximation in the SU(2) pure lattice gauge theory

The phase structure of the SU(2) pure lattice gauge theory with two coupling constants is derived in the mean-field approximation. The obtained phase diagram agrees with Monte Carlo results. The technique used here allows the computation of further corrections.