Unified study of lead: Energy-dependent pseudopotential calculation

A Unified study of lattice-mechanical properties of lead using energy-dependent pseudopotential is carried out. Energy dependence in pseudopotential is considered through the effective mass approximation; the pseudopotential model chosen is the local Heine-Abarenkov model potential. Properties studied include cohesive energy, equilibrium lattice parameter, second-order elastic constants, pressure derivative of second-order elastic constants, equation of state (atT=0 K), phonon-dispersion and effective two-body interaction. The results show fairly good agreement with experiment especially with a modified Heine-Abarenkov potential.     

On the Model Pseudopotential Approach to Calculate the Lattice Mechanical Properties of Thorium

The applicability of model pseudopotential approach to investigate lattice mechanical properties of Thorium, a typical f-shell metal, has been examined in light of some recent experimental and theoretical studies. It is found that presently available model potentials do not account for s-d-f hybridization adequately. The equation of state is greatly affected by s-d-f hybridization. It is also observed that a model potential giving reasonably good phonon dispersion curves may not reproduce equally good density of phonon states and hence the related lattice mechanical properties. However, it is possible to have a model potential, which may give fairly good estimate of lattice dynamical properties.     

Pseudopotential theory of thek-dependent plasmon line width in simple metals

The nearly free electron pseudopotential theory is used to calculate thek-dependent plasmon linewidth that results from the decay of plasmons via interband transitions. The theory predicts the linewidth to be anisotropic in crystalline systems fork 0. Local field effects are included, but are found to give very small contribution. A detailed analysis of the behaviour of the linewidth of Al is given and very good agreement with recent experimental data is obtained.     

Pseudopotential study of lattice parameter and heat of formation for substitutional alloys

Ashcroft’s empty core pseudopotential is applied to the substitutional alloy (K-CS) to calculate the heat of formation and lattice parameter over the entire concentration range. At any concentration the defect crystal is considered to be equivalent to a perfect crystal with a modified lattice parameter and the potential parameter for the defect crystal is calculated by using some suitable interpolation formula. The calculated results agree well with the available experimental results.     

Eliashberg theory with the external pair potential

Based on BCS model with the external pair potential formulated in a work Grigorishin (2017) [1], analogous model with electron-phonon coupling and Coulomb coupling is proposed. The generalized Eliashberg equations in the regime of renormalization of the order parameter are obtained. High temperature asymptotics and effect of Coulomb pseudopotential on them are investigated: as in the BCS model the order parameter asymptotically tends to zero as temperature rises, but the accounting of the Coulomb pseudopotential leads to existence of critical temperature. The effective Ginzburg-Landau theory is formulated for such model.     

Influence of surface affinity of planar walls on effective interaction between the wall and colloids

Using density functional theory, we investigate the effective interaction between a big colloid immersed in a sea of small colloids and a wall which has different affinity to the small colloids. Steele 10-4-3 potential is introduced to mimic both short-range repulsive and long-range attractive interactions between the wall and the small colloids. It is found that the surface affinity of the wall has a significant influence on the effective interaction. In the short-range repulsive case, the repulsion greatly enhances the big colloid-wall effective attraction, which sensitively depends on the concentration of small colloids, and is not sensitive to the repulsive strength. In the long-range attractive case, both the concentration of small colloids and the attractive strength have great effect on the effective interaction, and with an increase of the attractive strength, a strong repulsion may be induced when the big colloid is close to the wall. In low density limit of small colloids, the present results agree well with those of the Asakura and Oosawa(AO) approximation.     

Mayer function perturbation theory of effective interaction of charged colloids

In this paper, the effective interaction between charged colloids has been studied based on the standard Mayer function perturbation theory. With the formalism developed in this paper, the effective interaction as a function of Mayer functions and the correlation functions of the homogeneous microions is obtained. The asymptotic behaviour of the effective interaction at large distance is analysed in detail. It is found that at large distance the effective interaction is Yukawa like, provided the bare charge is replaced by the renormalised one. Exact expressions for the renormalised charge and the decay length as functions of the short-range part of the Mayer function and that of the correlation function of the homogeneous microions are obtained. With perturbation methods, it is easy to see how the effective interaction at large distance is affected by microion correlations and nonlinearity.     

Pseudopotential theory of the width of the long wavelength plasmon in simple metals

The full width at half maximum (FWHM) of long wave-length plasmons in simple metals is derived in a form convenient for application. The line width is a measure of the strength of the pseudopotential, and very good agreement with recent experimental measurements is found for a representative set of nearly-free-electron (NFE) metals. The dispersion of the FWHM is also discussed.     

Enhanced isospin dependence of the empirical particle-hole effective interaction

The separation betweenT=0 andT=1 centroids of the empirical effective interaction is fairly large for the (d ₃ ^2/−1 f _7/2)JT particle-hole interaction as compared to nearby (f _7/2)² JT and (d _5/2)² JT particle-particle interactions. This interesting feature of the empirical effective interaction is shown to arise as a consequence of renormalization of the effective interaction as one truncates the configuration space from (s−d)⁻¹(f−p)¹ to (d ₃ ^2/−1 f _7/2) and from (f−p)² and (s−d)² configurations to (f _7/2)² and (d _5/2)² respectively.     

Self‐consistent theory of dynamic melting of a vortex lattice

The dynamic melting of vortex lattices in type II superconductors is considered. A field‐theoretic formulation of the pinning problem allows the average over the quenched disorder to be performed exactly. A self‐consistent theory is constructed using a functional method for the effective action, allowing a determination of the pinning force and the vortex fluctuations. The phase diagram for the dynamic melting transition is determined numerically. In contrast to perturbation theory, the self‐consistent theory is in quantitative agreement with the prediction of a recent phenomenological theory and simulations and experimental data.     

The dimensionally reduced effective theory for quarks in high-temperature QCD

We show that QCD undergoes a partial dimensional reduction at high temperatures also in the quark sector. In the kinematic region relevant to screening physics, where the lowest Matsubara modes are close to their “mass shells”, all static Green functions involving both quarks and gluons are reproducible in the high-T limit by a renormalizable three-dimensional Lagrangian up to order ²(T) 1/1nT. This three-dimensional theory only contains explicitly the lightest bosonic and fermionic Matsubara modes, while the heavier modes correct the tree-level couplings and generate extra local vertices. We also find that the quark degrees of freedom that have been retained in the reduced theory are non-relativistic in the high-T limit. We then improve our result to order ⁴(T) through an explicit non-relativistic expansion, in the spirit of the heavy-quark effective theory. This effective theory is relevant for studying QCD screening phenomena with observables made from quarks, e.g. mesonic and baryonic currents, already at temperatures not much higher than the chiral transition temperature T_c.     

The effect of density dependent Av18 effective interaction on the ground state properties of heavy closed shell nuclei

The channel-dependent Argonne Av₁₈ effective two-body interactions (CDEI) which are generated through the lowest order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av₁₈ bare nucleon–nucleon potential are used to calculate the ground state properties of heavy closed shell nuclei such as ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb. The harmonic oscillator basis, and the local density approximation (LDA) are applied to create the relative and the center of mass dependent effective two-body potential. We get more binding with respect to the similar calculation with the Reid types potentials. It is tried to omit the LDA and perform full calculation with the Av₁₈CDEI for light nuclei. The results indicate that the LDA works quite well. It is also shown that in case of heavy closed shell nuclei and unlike our previous report with Reid68Day   interaction, the contributions of higher partial waves (J>2$J>2$) are very important for the calculations with Av₁₈ potential and we get reasonable agreement between our calculated binding energies and RMS radii, with those predicated by the others methods, and the experimental data. Finally, the various aspects of channel and density dependent two-body effective interactions are discussed.     

Local structure theory: Calculation on hexagonal arrays,and interaction of rule and lattice

Local structure theory calculations⁷ are applied to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway'sLife. The local structure theory captures many of the statistical properties of this rule; this supports hypotheses raised by a study ofLife itself⁽⁶⁾. As inLife, the state of a cell under (3422) depends only on the state of the cell itself and the sum of states in its neighborhood at the previous time step. This property implies that evolution rules which operate in the same way can be studied on different lattices. The differences between the behavior of these rules on different lattices are dramatic. The mean field theory cannot reflect these differences. However, a generalization of the mean field theory, the local structure theory, does account for the rule-lattice interaction.     

Electron-TO-phonon interaction in polar crystals

In the present work, the interaction between electrons and long-wavelength transverse optical (TO) vibrations in a polar insulator is considered. The crystal model employed for the theoretical analysis includes classical potentials and electronic polarizabilities. A significant enhancement of the strength of the electron-TO-phonon interaction in ferroelectrics has been found. A microscopic justification of this effect is given. A bridge that relates the interaction of electrons with the polar long-wavelength TO modes of lattice vibrations to the long-range dipole-dipole interaction is established. As an application of our analysis, a novel method for quantitative predictions of the electron-TO-phonon interaction constants in polar crystals via the data of experimental studies is suggested.     

Unified study of alkaline earth metal

A comprehensive unified study of fcc alkaline earth metal Ca, Sr and the bcc phase of Sr and Ba has been made. Properties studied include equilibrium lattice parameter, total crystal energy, second order elastic constants, pressure derivative of the second order elastic constants and phonon spectrum in the symmetry direction. The results obtained show an overall agreement with experiment. The results partially reproduced the experimentally observed phonon-crossover in Ba, and this has been found as the many-body effect in lattice dynamics.     

玻色爱因斯坦凝聚体中杂质的相互作用

文章研究了两个杂质浸入玻色凝聚体中的相互作用.通过使用微扰法,计算了在弱杂质-玻色子相互作用区域中的基态能量.结果表明基态能量与两杂质之间的相对距离有关.从基态能量出发,研究发现不管杂质与玻色子相互作用是处在排斥状态还是吸引状态,两杂质之间都有保持吸引趋势;而当一个杂质与玻色子相互作用是吸引时,另一个为排斥时,两个杂质之间呈现出了排斥的效果.通过杂质之间有效力的计算也验证了上述现象,进一步研究凝聚体密度背后的力学机制,再次得出了一致结论.     

Effective potentials in the Lifshitz scalar field theory

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling z=2, and the mass and the coupling constants renormalization are performed whereas the finite counterterm is just needed for the highest order of the coupling because of the mild UV divergence. Finally, we investigate whether the critical temperature for the symmetry breaking can exist or not in this approximation.