Bose--Einstein Condensates with Two- and Three-Body Interactions in an Anharmonic Trap at Finite Temperature

The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose-Einstein condensation （BEC） with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree-Fock-Bogoliubov （HFB） approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.     

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.     

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.     

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.     

Temperature Dependence of Retrograde Velocity of Vacuum Arcs in Magnetic Fields

Retrograde velocity of vacuum arcs in transverse magnetic fields is known to depend on, among other things, the magnetic induction, the arc current, the electrode spacing, the cathode material, and the cathode surface condition, and was also found to depend on the cathode temperature. Using the optical method, the retrograde velocity was measured as a function of the cathode temperature with copper, aluminum, and stainless steel as cathode materials. The optical measurement shows that by increasing the cathode temperature, the arc velocity decreases. It appears that with the increase in the cathode temperature, the decrease of the arc velocity is related to the increase of the cathode crater radius. The experimentally measured temperature dependence of the retrograde velocity of vacuum arcs can be explained by the ion jet model for retrograde motion of vacuum arcs [10]. The relative decrease of retrograde velocity as a function of the cathode temperature calculated according to this model agrees quantitatively with the reported measurements.     

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s~udied in details.     

Effects of QCD Vacuum and the Instanton Induced-Contributions to the Nucleon Structure Functions

The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F2 (x, Q2 ), is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, ρ, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x0.1 which confirms the validity of our calculations.     

Vacuum Condensates and the Anomalous Magnetic Moment of a Dirac Fermion

We address anticipated fermion–antifermion and dimension-4 gauge-field vacuum-condensate contributions to the magnetic portion of the fermion–photon vertex function in the presence of a vacuum with nonperturbative content, such as that of QCD. We discuss how inclusion of such condensate contributions may lead to a vanishing anomalous magnetic moment, in which case vacuum condensates may account for the apparent consistency between constituent quark masses characterizing baryon magnetic moments and those characterizing baryon spectroscopy.     

Dynamics of Two- and Four-Boson Interactions in Dressed Vacuum States

We analyze the spatial and temporal dynamics of virtual particles in the vacuum states of the one-dimensional ? ²- and ? ⁴-model systems. The properties of the vacuum state for the ? ²-system can be found analytically, which allows us to compute all spatial and temporal correlations exactly. For large spatial and temporal separations, the correlation functions approach a non-vanishing finite constant associated with the occurrence of multiple vacuum bubbles, in contradiction to lowest-order perturbation theory. Long-range inter-bubble correlations suggest that virtual particles can actually enhance the occurrence of another bubble due to stimulated emission. We argue that many of the vacuum’s properties can be explained in the usual particles terms.     

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.     

The Scalar Photon Light-Cone Distribution Amplitude in the Instanton Vacuum Model of QCD

Based on the principle of the Lorentz covariance, the transition matrix elements from an off-shell photon state to the vacuum are parameterized by the light-cone photon distribution amplitudes （DAs）. Both the scalar off-shell photon light-cone DA and the corresponding coupling are calculated in the instanton vacuum model of quantum chromodynamics （QCD）, and their explicit analytical expressions and the numerical results are given. The results for the other chiral-odd light-cone photon DAs and their couplings are presented as well.     

Dynamically Running Mass of Light Quark and QCD Vacuum Condensates

Based on Dyson-Schwinger equations (DSEs) in “rainbow“ approximation, the dynamically running mass of light quark and QCD vacuum condensate are investigated. The structure of non-local quark vacuum condensate, the values of local vacuum condensate of quarks and quark-gluon mixture, and dynamical transition of quark mass from current quark to constituent quark are illustrated. At the same time, according to the knowledge and experience learned from an extensive study of the solutions of DSEs, a parameterized form of confining quark propagator is suggested for a practical use. The new parameterized form of quark propagator is analytic everywhere in the finite complex p2-plane and has no Lehmann representation. The predictions for p2-dependence of effective quark masses, Mf(p2), defined by the self-energy functions Af(p2) and Bf(p2), both from the numerical solutions of DSEs and from its parameterized form, are shown dynamically. Our conclusion is that all numerical results are consistent with empirical values used in QCD sum rules and lattice QCD calculations. For a qualitative study, the parameterized form is a sufficiently good approximation to confining quark propagator.     

夸克的真空凝聚值和张量感应率及参数化的夸克传播子

利用以前提出的参数化的夸克传播子， 计算了夸克的真空凝聚值和QCD真空的张量感应率。 结果表明， 张量感应率对不同味道的夸克的依赖是很明显的， 而几乎不依赖于夸克的真空凝聚值的变化。 但夸克凝聚值却明显地与积分的截断值有关， 即依赖于微扰区与非微扰区的分界线， 在常用的积分截断值1—2 GeV2之间计算得到的夸克凝聚值与文献中常用的值及其他理论的预言值是一致的。 理论预言的张量感应率也与其他理论结果相一致。     

Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio （NJL） model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark ,condensates in vacuum also depends on Gs/Hs, the ratio of the coupling constants in scalar quarkantiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if Gs/Hs 〉 2/3, which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if 0 〈 Gs/Hs 〈 2/3. However, different from the 4D NJL model, the pure diquark condensates arise only at Gs/Hs = 0 and are not in a possibly finite region of Gs/Hs below 2/3.     

Interplay Between Quark-Antiquark and Diquark Condensates in Vacuum in a Two-Flavor Nambu-Jona-Lasinio Model

By means of a relativistic effective potential, we analytically research competition between the quark- antiquark condensates （qq） and the diquark condensates （qq） in vacuum in ground state of a two-flavor Nambu Jona Lasinio （NJL） model and obtain the Gs-Hs phase diagram, where Gs and Hs are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure （qq） phase when Gs/Hs 〉 2/3, and as Gs/Hs decreases to 2/3 〉 Gs/Hs ≥ 0 one will first have a coexistence phase of the condensates （qq） and （qq） and then a pure （qq） phase. In non-zero bare quark mass case, the critical value of Gs/Hs at which the pure （qq） phase will transfer to the coexistence phase of the condensates （qq） and （qq） will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting sma/lest ratio Gs/Hs after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.     

Light 0- Meson Solution of Bethe-Salpeter Equation Involving the Vacuum Condensates in QCD

We dkcuss the Bethe-Salpeter equation involving the vacuum condensates in QCD in the backgrouud fields. The bound state equation for the light 0^- meson (π and K) is solved in the ladder approximation of single gluon exchange, where the gluon propagator is calculated in tree level of a gluon condensate and a quark condensate. The kernel is divided into two parts: perturbative and non-pert,urbative. The non-perturbative part is determined by the vacuum condensate. Pseudo-scalar meson spectrum and decay constants are in good agreement with data.     

Instanton in the Georgi-Glashow model

Topologically nontrivial solutions in the Georgi-Glashow model are studied. It is shown that only in quantum theory does an instanton exist as a stable field configuration. An effective action is constructed, and quantum equations of motion for the instanton are obtained on its basis. Their solutions at long and short distances are obtained. A critical size corresponding to a stable instanton in the Georgi-Glashow model is found.     

Instanton screening in the nonperturbative QCD

The gluon field screening in the stochastic vacuum of gluodynamics is studied. The effective action is derived for the instanton interacting with nonperturbative fields. Quantum nonperturbative effects are shown to affect greatly the shape of instanton. The power asymptotics x ⁻² of the classical “instanton’s profile function” at large distances is replaced due to these effects by Airy function asymptotics.     

Quark-Antiquark and Diquark Condensates in Vacuum in Two-Flavor Four-Fermion Interaction Models with Any Color Number Nc

The color number Nc-dependence of the interplay between quark-antiquark condensates （q^-q） and diquark condensates （qq） in vacuum in two-flavor four-fermion interaction models is researched. The results show that the Gs-Hs （the coupling constant of scalar （q^-q）2-scalar （qq）2 channel） phase diagrams will be qualitatively consistent with the case of Nc = 3 as Nc varies in 4D Nambu-Jona-Lasinio model and 219 Gross Neveu （GN） model, However, in 3D GN model, the behavior of the Gs-Hp （the coupling constant of pseudoscalar （qq）^2 channel） phase diagram will obviously depend on No. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates （q^-q） and （qq） is proven to appear only in the case of Nc ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates （qq） in corresponding phase diagrams will gradually decrease as Nc grows up and finally go to zero if Nc → ∞, i.e. in this limit only the pure （q^-q） phase could exist.