A Model Study of Equation of State of QCD at Finite Chemical Potential and Zero Temperature

In this paper, we give a direct method for calculating the partition function, and hence the equation of state （EOS） of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms： the first term P（μ）｜μ=0 （the pressure density at μ = 0） is a μ-independent constant; the second term, which is totally determined by G[μ] （p） （the dressed quark propagator at finite μ）, contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71 （2005） 015205], G[μ]（p） is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 67 （2003） 054019]. From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained （apart from the constant term P（μ）｜μ=0, which can in principle be caJculated from the CJT effective action）. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.     

Adsorption isotherm of a Lennard-Jones nitrogen in a carbon slitlike pore

A density functional perturbation approximation based both on second-order perturbation theory and on the pore average density has been proposed to study the adsorption hysteresis of nitrogen in a carbon slit pore. The main advantage of the present approximation is that it is computationally much simpler than the original density functional approximation based on the second-order perturbation theory of liquids, and can be applied to several model fluids confined in a strong external field in order to study their structural and thermodynamic properties. The calculated adsorption hysteresis for the confined Lennard-Jones nitrogen is in very good agreement with computer simulation, even if its accuracy slightly deteriorates for the desorption branch. The calculated equilibrium particle density distributions also compare well with computer simulations, and are better than those of a density functional theory based on the so-called mean-field approximation.     

Calculation of equation of state of QCD at zero temperature and finite chemical potential

In this paper we calculate the equation of state (EOS) of QCD at zero temperature and finite chemical potential by using several models of quark propagators including the Dyson-Schwinger equations (DSEs) model, the hard-dense-loop (HDL) approximation and the quasi-particle model. The results are analyzed and compared with the known results in the literature.     

A rearrangement of the Feenberg perturbation formula and elementary excitation interactions in bose fluids

The Feenberg perturbation energy for two quasiparticle excitations is rearranged to be valid in many-boson systems up to fifth order. Doubly excited states in many particle boson systems are studied using Feenberg perturbation theory. The effective interaction energy between quasiparticles, which is described by “ladder state diagrams” — in Bogoliubov approximation, is obtained. It is then shown that in this case the interaction energy depends on density (pressure) and changes its sign when density increases if the bare two-body potential qualitatively has short range repulsion and longer range attraction.     

加压下ZnO结构相变和电子结构的第一性原理计算

基于密度泛函(DFT)理论的第一性原理,计算半导体ZnO纤锌矿结构和岩盐矿结构状态方程及其在高压下的相变,分析加压下体相ZnO的晶格常数、电子态密度和带隙随压力的变化关系,并将计算结果与文献中的理论和实验数据进行比较.验证在计算金属氧化物时,应用局域密度(LDA)近似计算出的相变压力普遍偏高,采用广义梯度(GGA)近似得到的结果与实验符合较好.     

GaAs相变和热力学性质的密度泛函理论研究

利用平面波赝势密度泛函方法,对GaAs从闪锌矿结构到CsCl 结构的相变进行了理论研究.通过Birch-Murnaghan状态方程拟合闪锌矿结构GaAs的能量和体积,得到了GaAs的热力学性质.我们发现对 GaAs来说,闪锌矿结构通常比CsCl结构稳定,由闪锌矿结构到CsCl结构的相变压力在37.019 GPa左右.计算所得到的晶格常数、体弹模量及体弹模量对压强的一阶导数与实验值以及其他作者的计算值相符合.     

Lattice dynamics properties of zinc-blende and Nickel arsenide phases of AlP

Ab initio calculations, based on norm-conserving non-local pseudopotentials and the density functional theory (DFT), have been performed to investigate the behaviour under hydrostatic pressure of the structural, electronic, elastic and dynamical properties of AlP, in both zinc-blende and nickel arsenide phases. Our calculated structural and electronic properties are in good agreement with previous theoretical and experimental results. The phonon dispersion curves, the elastic constants, Born effective charge, etc., were calculated with the local density approximation and the density functional perturbation theory (DFPT). Our results in the pressure behaviour of the elastic and dynamical properties of both phases are in agreement with the experimental data when available, in other case they can be considered as predictions.     

First-principles study of the anisotropic thermal expansion of hcp metals Be and Y

A first-principles study of the anisotropic thermal expansion of hcp metals Be and Y is reported. According to quasiharmonic approximation, the phonon spectra were computed at a set of lattice parameters using the pseudopotential plane wave method with the local density approximation in the framework of the density functional perturbation theory. The free energies were obtained according to the calculated phonon spectra and thermal properties such as specific heat at constant volume (pressure) were calculated. The electronic contribution to specific heat was found important to metal Y not only at very low temperature but also over room temperature. The calculated results are in good agreement with available experimental data in a wide range of temperature.     

Thermodynamic properties of the Lennard-Jones FCC solid: perturbation theory parameterisation and Monte Carlo simulation

This work is concerned with a valid representation of the solid-phase equation of state (EOS), the validity of which is evaluated by comparing to Monte Carlo (MC) simulation results. The proposed EOS has been developed by employing an optimal division of the Lannard-Jones (LJ) potential and an effective temperature- and density-dependent diameter into the framework of the simplified perturbation theory. Then, with the aim of extending to the chain systems, the conventional chain contribution (i.e. TPT1) is added to the proposed model (i.e. the atomic LJ system). Finally, the solid-state EOS based on Helmholtz free energy will be introduced for low temperature and high density conditions. To verify the accuracy of the proposed model, its performance is compared with the results of MC simulation. The comparison between the obtained results from the proposed model and the MC simulations shows that the EOS can satisfactorily predict the properties of the solid LJ system, both for the atomic system and for the chains.     

混合物物态方程的计算

 在采用体积相加原理计算混合物物态方程的基础上,建立了一种物理模型确定混合物温度。根据混合物中各组分温度和压强平衡条件,采用压强-密度迭代方法计算给出混合物物态方程,编制了两种组分的混合物物态方程计算程序。为检验建立的温度模型的合理性及程序的有效性,分析了不同密度、温度状态的氢（H2）和钨（W）组成的混合物状态参量,计算了以下情形及其组合情形的混合物物态方程：H₂和W以不同质量比混合;质量比固定,单组分状态不同;温度区间和密度区间不同。研究表明:实际应用中在建立的混合物温度模型基础上确定的混合物物态方程是合理的。     

Thermodynamics of wurtzite GaN from first-principle calculation

The density function perturbation theory (DFPT) is employed to study the linear thermal expansion and heat capacity at constant pressure (with the quasiharmonic approximation) for wurtzite GaN. The calculated results of linear thermal expansion coefficient and heat capacity at constant pressure are compared with the available experimental data in a wide temperature range. Generally these properties calculated agree well with experimental data except at high temperature, thus it suggests the thermal expansion and heat capacity can be well calculated from this first-principle approach.     

广义Morse流体解析状态方程及对氮的应用

 根据Ross变分微扰理论以及硬球流体Percus-Yevick（PY） 径向分布函数表达式,建立了广义Morse势流体的解析状态方程。与模拟结果的比较一方面证实了广义Morse 势模型的合理性;另一方面表明了解析Ross变分微扰理论的精度相当或略好于非解析的Weeks-Chandler-Anderson （mWCA）理论,而优于复杂的优化超网络链积分方程理论（RHNC）。该解析状态方程被应用于拟合处于环境温度和压强小于1 GPa情形流体氮的实验数据,所得到的势能参数被用于预测高温高密度情形氮流体的压强,预测结果证实,该解析状态方程可以很好地适用于较宽的压强和温度范围。     

致密物质性质和适用于超新星及中子星研究的状态方程(英文)

采用相对论平均场方法研究了致密物质的性质, 构造了包括较宽温度、 同位旋不对称度和密度范围的适用于超新星模拟研究的状态方程, 均匀物质由相对论平均场理论描述, 非均匀物质由托马斯 费米近似给出。讨论了包含超子自由度的中子星物质的状态方程。 计算结果表明, 包含超子可以有效地软化高密度区的状态方程, Λ超子的超流态有可能存在于大质量中子星内部。The properties of dense matter are studied within the relativistic mean field theory. The equation of state (EOS) of dense matter are constructed covering a wide range of temperature, proton fraction, and density for the use of supernova simulations. The relativistic mean field theory is employed to describe the uniform matter, while the Thomas Fermi approximation is adopted to describe the non uniform matter. The EOS of neutron star matter is discussed with the inclusion of hyperons. It is found that the EOS at high density can be significantly softened by the inclusion of hyperons. The 1S₀ superfluidity of Λ hyperons may exist in massive neutron stars.     

Phase transition,lattice dynamical and thermodynamic properties of yttrium antimonide with the rock salt structure under high pressure: first-principles investigations

We investigate the structural, electronic, first-order pressure-induced phase transition, lattice dynamical, and thermodynamic properties of yttrium antimonide (YSb) with the rock salt structure at high pressures and high temperatures using the projector-augmented wave method based on the density-functional theory. By the usual condition of equal enthalpy, we find that the rock salt-structured YSb is stable up to 31.10 GPa, and then transforms to the CsCl-type structure, this is consistent with the experiment result which begins transform from 26 GPa then ends at 36 GPa. The phonon dispersion curves of the rock salt-structured YSb are calculated under high pressure for the first time using a linear-response approach to density-functional perturbation theory successfully. Within the calculated phonon density of state and the quasi-harmonic approximation, we predict further the thermal physical properties of YSb under high temperature and high pressure systematically.     

QCD PERTURBATION THEORY AND NUCLEI (1) THE ENERGY SHIFTS OF HADRENS AND HADRONS MASS DIFFERENCE MASS DIFFERENCE

QCD perturbation theory for confined quarks and gluons (inhadrons) is discussed.Based on the equivalent potential for the quark-gluon interaction derived, the energyshifts of hadrons and hadron mass difference in MIT bag (cavity) model and correcpond-ing approximation of the w. f. with Gassian form are calculated.     

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.     

Elastic and piezoelectric properties, sound velocity and Debye temperature of (B3) boron–bismuth compound under pressure

Pseudopotential plane-wave method (PP–PW) based on density functional theory (DFT) and density functional perturbation theory (DFPT) within the Teter and Pade exchange-correlation functional form of the local spin density approximation (LSDA) is applied to study the effect of pressure on the elastic and piezoelectric properties of the (B3) boron–bismuth compound. The phase transition, the independent elastic stiffness constants, the bulk modulus, the direct and converse piezoelectric coefficients, the longitudinal, transverse, and average sound velocities, and finally the Debye temperature under pressure are studied. The results obtained are generally lower than the available theoretical data (experimental data are not available) reported in the literature.     

Structural, electronic and vibrational properties of InN under high pressure

The structural, electronic and vibrational properties of InN under pressures up to 20 GPa have been investigated using the pseudo-potential plane wave method (PP-PW). The generalized-gradient approximation (GGA) in the frame of density functional theory (DFT) approach has been adopted. It is found that the transition from wurtzite (B4) to rocksalt (B1) phase occurs at a pressure of approximately 12.7 GPa. In addition, a change from a direct to an indirect band gap is observed. The mechanism of these changes is discussed. The phonon frequencies and densities of states (DOS) are derived using the linear response approach and density functional perturbation theory (DFPT). The properties of phonons are described by the harmonic approximation method. Our results show that phonons play an important role in the mechanism of phase transition and in the instability of B4 (wurtzite) just before the pressure of transition. At zero pressure our data agree well with recently reported experimental results.     

Correlation corrections based on the Schrödinger equation with a local potential

A compromise version of calculation of the ground state electronic energy is proposed that combines both the density functional theory and the wave function formalism. Single-particle orbitals and energies are determined by solving the Kohn-Sham equations with a local effective potential, which depends on the parameters determined by the variational principle. Correlation corrections are calculated using the Rayleigh-Schrödinger perturbation theory in the zero-order approximation of the Möller-Plesset theory. The specific features of the expressions for the corrections to the wave function and the energy determined in terms of the Kohn-Sham orbitals are considered. This approach, in contrast to the well-known optimized effective potential method, can be applied with equal computational expenditures to both atoms and molecules. A comparative analysis for 20 helium-like atoms showed that the scheme proposed provides better agreement with the “exact” values of the energy in the second order of the perturbation theory in comparison with the results obtained using the conventional exchange-correlation potentials BLYP and PW91. A similar trend is also observed for diatomic hydrides (from LiH to FH), although, in contrast to the atoms, the deviations from the experimental estimates of the energy are less systematic.     

Structural and Thermodynamic Properties of TiAl intermetallics under High Pressure

The structural and thermodynamic properties of TiAl intermetallics under high pressure have been investigated by ab initio plane-wave pseudopotential density functional theory method.It is found that the ratio of lattice parameter c to a keeps almost constant with a value of 1.02 under the pressure from 0 to 20 GPa,which agrees well with the experimental results.With the pressure increasing from 20 to 45 GPa the values of c/a decrease almost linearly from 1.02 to 0.99.These calculated results indicate under low pressure the variation rate for a-axis is almost the same to that for c-axis,but under higher pressure the variation for a-axis is smaller than along c-axis.Through the quasi-harmonic Debye model,the equation of state(EOS) of TiAl intermetallics,as well as the thermal expansion and heat capacity at various pressures and temperatures are also studied.