Vacuum Condensates from the Modification of Global Color Symmetry Model

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate , the mixed quark gluon condensate g,μνσ^μνq) and the four-quark condensate at the mean-field level in the framework of global color symmetry model. The numerical calculation shows that our result is compatible with the range obtained within other nonperturbative approaches. In particular, we have found that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.     

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.     

Tensor Vacuum Susceptibility

Using a nonlocal four-quark condensate in the framework of the modified global colour symmetry model, we determine the tensor vacuum susceptibility needed in the QCD sum rule external field method for the coupling of tensor current to hadron and compare it with the previous estimations.     

Modified Approach for Calculating Four-Quark Condensates

By differentiating the dressed quark propagator with respect to a variable background field,the linear response of the dressed quark propagator in the presence of the background field can be obtained.From this general method,using the vector background field as an illustration,we extract a general formula for the four-quark condensate〈(0)|-q(0)γμq(0)-q(0)γμq(0)|0〉.This formula contains the corresponding fully dressed vector vertex. We use this formula to analyze the factorization problem of the four-quark condensate and show that in the bare vertex approximation factorization holds exactly.     

Convergence of mean-field approximations in site percolation and application of CAM tod=1 further-neighbors percolation problem

We study the mean-field approximation in the site-percolation problem. Using the analog of the Simon-Lieb inequality, we show that the mean-field critical probability is convergent to the exact value when the size of clusters tends to infinity. Applying this approximation to the one-dimensional further-neighbor percolation problem and calculating some critical coefficients, we prove that the asymptotic scaling relations predicted by the coherent-anomaly method are satisfied.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.     

Phase diagram of neutron star quark matter in nonlocal chiral models

We analyze the phase diagram of two-flavor quark matter under neutron star constraints for a nonlocal covariant quark model within the mean-field approximation. Applications to cold compact stars are discussed.     

相对论无规位相近似

讨论了建立在相对论平均场基态的相对论无规位相近似研究中的一致性问题. 研究表明考虑费米海和Dirac海的粒子 空穴激发对核的同位旋标量巨共振的能量有很大的影响. The fully consistent relativistic random phase approximation (RRPA) built on the relativist mean field (RMF) ground state is presented. The fully consistent RRPA requires that the nuclear RMF wave function and the RRPA renormalization are calculated in a same effective Lagrangian. A theoretically complete treatment of the RRPA at the mean field level with no sea approximation must include not only the usual particle hole states, but also the pairs formed from the occupied Fermi states and Dirac states. Effects of inclusion of Dirac sea states in various multipole excitations are investigated. Considerable effects on the isoscalar giant multipole resonances are observed.     

虚光场对双模压缩真空场与原子相互作用系统纠缠特性的影响

研究了非旋波近似下双模压缩真空场与二能级原子相互作用系统的纠缠特性,着重讨论了虚光场效应对系统纠缠特性的影响.     

Critical properties of the half-filled Hubbard model in three dimensions

By means of the dynamical vertex approximation (DΓA) we include spatial correlations on all length scales beyond the dynamical mean-field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to nonlocal fluctuations are (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)ferromagnet and (ii) a sizable reduction of the Néel temperature (T(N)) by ~30% for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between DΓA and DMFT in different regions of the phase diagram.     

Matrix elements of four-quark operators relevant to life time difference \Delta \Gamma _{B_s} from QCD sum rules

We extract the matrix elements of four-quark operators relevant to the and life time difference from QCD sum rules. We find that the vacuum saturation approximation works reasonably well, i.e., within 10%. We discuss the implications of our results and compare them with a recent lattice QCD determination. Received: 23 April 2001 / Revised version: 27 May 2001 / Published online: 19 July 2001     

具有时滞状态反馈的随机Van der Pol系统的动力学研究

研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响. 运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件, 同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果. 通过与平均场近似下的解析结果比较后发现, 数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响. 关键词： 平均场近似 关联时间 Lyapunov稳定性     

格点规范场的真空波函数和真空能量的无规相近似计算

采用无规相近似(RPA)耦合集团展开方法,计算出2?+1维SU(2?)格点规范场的三到六阶真空波函数和真空能量.在计算中,用空心图构成试探波函数,得到的三到六阶真空波函数的计算结果在弱耦合区1g²〉1.2都表现出良好的标度行为.与较早的计算结果比较,采用RPA方法计算的真空波函数比采用非RPA方法计算的结果的标度行为有大幅度的改善.采用RPA方法计算的真空能量比采用非RPA方法计算的真空能量略低,这表明此方法是成功的方法.     

Stochastic dynamics in a two-level model of disorder: comparison of mean-field and exact solutions

Stochastic dynamics in the presence of quenched disorder (e.g., diffusion in a random medium) is generally treated in a suitable mean-field or effective medium approximation. While numerical simulations may help determine the accuracy of such approximations in specific models, there are relatively few instances in which analytic solutions are possible, to enable a precise comparison to be made with the mean-field results. We consider in this paper a simple but general model of quenched disorder in which a system variablex jumps stochastically between two valuesx _a andx _b . However, in each level there occurs with a certain probability a branch (or internal) state into which the system may fall, and from which a jump to the other level is possible only after a return to the original (or ‘active’) state. Four different configurations of the states of the system are thus possible, and the transitions between the states are governed by Markovian transition probabilities. The moments ofx and its autocorrelation function are computed in each case, and then configuration-averaged over the four realizations. This represents the exact solution. Next, a mean-field theory of the dynamics is developed: this turns out to involve an effective waiting-time density at each of the two levels that is non-exponential in time, so that the mean-field dynamics is a non-Markovian alternating renewal process. The moments and autocorrelation ofx are again computed, and compared with the exact solutions. The extent of the differences at both short and long times is elucidated, and a numerical comparison is presented for the case of maximal disorder.     

Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.     

Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation

A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity-intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.     

Particle Production in Expanding Spacetime

The complex time WKB (CWKB) approximation has been an effective technique to study particle production in expanding space time. The success of the approximation technique both in time and space dependent gauge has motivated us to study the method in relation to the time dependent approximation. In this work we try to understand the adiabatic and non-adiabatic transition within the framework of complex time WKB approximation. We find that the emergence of thermal radiation is due to some topological characteristics of cosmological spacetime that separates the spacetime into Euclidean and non-Euclidean region. This applies also to blackhole spacetime. The complex WKB trajectory approach shows that the Euclidean vacuum fluctuation is root cause of thermal particle production and is basically a Hawking effect. We also study here the sensitivity of particle production on the rise of scale factor at early times. It is found that the tunneling paths are responsible for the origin of thermal radiation whereas the slope of the scale factor determines the magnitude of the temperature of the thermal particle production. We also substantiate Hu's assertion in this connection.     

Massive Meson Fluctuation in NJL Model

Based on the self-consistent scheme beyond the mean-field approximation in the large N_c expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of N_c,an approximate internal meson propagator is deduced, which is in order of O(l/N_c). In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show that, different &om the mean-field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond the meanfield approximation.     

The ambivalent effect of lattice structure on a spatial game

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect’ (ALLD), ‘tit-for-tat’ (TFT), and ‘always cooperate’ (ALLC) plays the repeated Prisoner’s Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.     

Poissonian Behavior of Ising Spin Systems in an External Field

We apply the Stein–Chen method for Poisson approximation to spin-half Ising-type models in positive external field which satisfy the FKG inequality. In particular, we show that, provided the density of minus spins is low and can be expanded as a convergent power series in the activity (fugacity) variable, the distribution of minus spins is approximately Poisson. The error of the approximation is inversely proportional to the number of lattice sites (we obtain upper and lower bounds on the total variation distance between the exact distribution and its Poisson approximation). We illustrate these results by application to specific models, including the mean-field and nearest neighbor ferromagnetic Ising models.