Linear Chemical Potential Dependence of Two-Quark Condensate

By differentiating the inverse dressed quark propagator at finite chemical potential μ with respect to μ, the linear response of the dressed quark propagato r to the chemical potential can be obtained, From this we extract a modelindependent formula for the linear chemical potential dependence of the in-medium two-quark condensate and show by two independent methods （explicit calculation and Lorentz covariance arguments） that the first-order contribution in μ to the in-medium two-quark condensate vanishes identically. Therefore if one wants to study the in-medium two-quark condensate one should expand to at/east the second order in the chemical potential μ.     

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential （μ = 0） and neglecting the #-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 （2005） 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 （1998） 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann Oakes-Renner relation also holds at finite chemical potential     

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential (μ=0) and neglecting the μ-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 (2005) 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ=0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 (1998) 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann-Oakes-Renner relation also holds at finite chemical potential.     

非定域夸克真空的结构和Kisslinger函数

夸克的真空凝聚是量子色动力学(QCD)研究中一个非常重要的问题.用完全穿衣服的夸克传播子研究了QCD真空性质和夸克的真空结构.计算了定域夸克的真空凝聚值,预言了夸克的真空结构.其结果与文献中的经验值相符合,也与Dyson-Schwinger方程解一致.说明参数化的夸克传播子是成功和可靠的.     

Chemical Potential Dependence of Two-Quark Condensates

By adopting the background field method, the response of the dressed quark propagator to the presence of finite chemical potential is analysed up to the second order. From this, we obtain a model-independent formula for the chemical potential dependence （up to the second order） of the in-medium two-quark condensate and show by both Lorentz covariance arguments and explicit calculations that the O（μ） contribution to the in-medium two-quark condensate vanishes identically.     

Bose-Einstein Condensate in a Linear Trap with a Dimple Potential

We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.     

Two-Quark Condensate Changes with Quark Current Mass

Using the Schwinger-Dyson equation and perturbation theory, we calculate the two-quark condensates for the light quarks u, d, strange quark s and a heavy quark c with their current masses respectively. The results show that the two-quark condensate will decrease when the quark mass increases, which hints the chiral symmetry may be restored for the heavy quarks.     

Chemical Potential Dependence of Dressed-Quark Propagator

A method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model is developed.Of particular interest here is to give a general recipe to find without arbitrariness the solution representing the “Wigner”phase at non-zero chemical potential for the purpose of studying QCD phase structure.     

Two-Quark Condensate Changes with Quark Current Mass

Using the Schwinger Dyson equation and perturbation theory, we calculate the two-quark condensates for the light quarks u, d, strange quark s and a heavy quark c with their current masses respectively. The results show that the two-quark condensate will decrease when the quark mass increases, which hints the chiral symmetry may be restored for the heavy quarks.     

Quark Gluon Condensate, Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in ＂rainbow＂ approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Quark Gluon Condensate,Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in “rainbow” approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson-Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.     

Fermion-Boson Vertex at Finite Chemical Potential

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analyms, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the frmionboson vertex in QED at finite chemical potential.     

Analytic Method to Study Influence of Finite Chemical Potential in QED3

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED3. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemieal potential is investigated.     

Chemical Potential Dependence of the Dressed-Quark Propagator from an Effective Quark-Quark Interaction

We exhibit a method for obtaining the low chemical potential dependence of the dressed quark propagatorfrom an effective quark-quark interaction model. Within this approach we explore the chemical potential dependenceof the dressed-quark propagator, which provides a means of determining the behavior of the chiral and deconfinementorder parameters. A comparison with the results of previous researches is given.     

Calculation of Four-Quark Condensate Beyond Vacuum Saturation Approximation

Based on a modification of theaglobal color symmetry model, we have calculated the four-quark condensate beyond vacuum saturation approximation by including the contribution of r and u mesons. The numerical results show that there is a sizeable correction of the four-quark condensate in comparison with its factorized value using the vacu urn saturation approximation.     

Chemical Potential Dependence of the Dressed—Quark Propagator from an Effective Quark—Quark Interaction

We exhibit a method for obtaining the low chemical potential dependence of the dressed quark propagator from the dressed-quark propagator,which provides a means of determining the behavior of the chiral and deconfinement order parameters.A comparison with the results of previous researches is given.     

夸克胶子混合真空凝聚和Dyson-Schwinger方程

基于夸克传播子的Dyson-Schwinger方程，计算了夸克胶子混合真空凝聚和夸克真空凝聚. 这些凝聚不仅联系着夸克在真空态中的虚度，而且也表征了真空中夸克分布的空间宽度. 真空凝聚的存在直接反映着QCD真空的非微扰结构. 计算表明：上夸克与下夸克的虚度为λ²_u,d=0.7GeV²，奇异夸克的虚度为λ²_s=1.6GeV². 这些结果与许多用完全不同的方法得到的结果一致.     

共振粒子的化学势和粒密度、能密度

研究了相对论重离子碰撞中产生的共振物质的统计性质，讨论了共振粒子的化学势和净粒子密度的关系. 计算了总粒子密度和能量密度，研究和分析了他们和净粒子密度的关系，并估算了总粒子密度相对于正常核密度(0.16fm－3)的倍数；在RHIC能量约为5-8倍，在SPS能量约为3-6倍. 还研究了各种粒子成分随温度的变化，揭示出几个温度区间段对应AGS、SPS和RHIC三个能区，各区间中主要粒子成分分别为重子、奇异子和介子.     

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.     

QCD真空凝聚和参数化的夸克传播子

基于整体色对称模型,用完全穿衣服参数化的夸克传播子研究了量子色动力学(QCD)真空的性质,预言了各种表征QCD真空的凝聚值.其结果与其他唯象QCD理论模型的预言是一致的.结果清楚地表明了参数化的夸克传播子是成功和可靠的.讨论了计算QCD真空凝聚值时积分截断参数的问题,提出了一个避免计算的结果对截断参数强烈依赖的物理方法.