Numerical Evaluation of a Two-Loop Diagram in the Cutoff Regularization

The sunset diagram of λΦ^4 theory is evaluated numerically in cutoff scheme and a nonzero finite term (in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This finding dramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in our previous work.     

On the Equivalence of Regularization Schemes

We illustrate via the sunset diagram that dimensional regularization ‘deforms‘ the nonlocal contentsof multi-loop diagrams with its equivalence to cutoff regularization scheme recovered only after sub-divergence wassubtracted. Then we employed a differential equation approach for calculating loop diagrams to verify that dimensionalare argued especially in nonperturbativc perspective.     

Goldstone boson counting in relativistic systems at finite density

We study the effects of finite chemical potential on the pattern of symmetry breaking within the relativistic linear sigma model. In accordance with previous works we show that type-II Goldstone bosons may appear whose dispersion relation is quadratic in momentum in the long-wavelength limit. We show that their presence is tightly connected with nonzero densities of non-Abelian Noether charges, and formulate a general counting rule for the number of the Goldstone bosons. Working at tree level, we conclude with the discussion of the loop effects. Our results find an application in particular to cold dense quark matter, where a type-II Goldstone boson has been found, e.g., in the phases with kaon condensation.     

Ambiguities in the Regularization of the Spiked Harmonic Oscillator

It has been suggested that the machinery of PT-symmetric quantum mechanics can be utilized to regularize certain singular potentials. In this contribution I point out that different regularizations lead to different results. In a particular model, that of the spiked harmonic oscillator, I use a symmetry inherent in the model to cast some light on this ambiguity.     

Leading logarithms in the anomalous sector of two-flavour QCD

We add the Wess–Zumino–Witten term to the N=3$N=3$ massive nonlinear sigma model and study the leading logarithms in the anomalous sector. We obtain the leading logarithms to six loops for π⁰→γ^?γ^?${\pi }^0\to {\gamma }^{?}{\gamma }^{?}$ and to five loops for γ^?πππ${\gamma }^{?}\pi \pi \pi$. In addition we extend the earlier work on the mass and decay constant to six loops and the vector form factor to five loops. We present numerical results for the anomalous processes and the vector form factor. In all cases the series are found to converge rapidly.     

实验探索原子核中手征与空间反射对称性的联立自发破缺

原子核的手征对称性和空间反射对称性研究是近来原子核结构研究的前沿热点问题,吸引了大量的实验和理论研究。通过在束伽玛谱学的实验方法,在原子核78Br中发现了两对宇称相反的手征双重带,以及它们之间表征八极关联的电偶极跃迁。这是首次在原子核中发现了八极关联的多重手征带,给出了原子核存在手征对称性和空间反射对称性联立自发破缺的实验证据。Spontaneous symmetry breaking is a fundamental concept in nature. Chiral Symmetry Breaking and reflection-asymmetry in nuclei has been a subject of intensive experimental and theoretical investigation. Two pairs of positive-and negative-parity doublet bands together with eight strong electric dipole transitions linking their yrast positive-and negative-parity bands have been identified in 78Br by means of in-beam gamma-ray spectroscopy techniques. These four rotational bands are suggested as multiple chiral doublet bands with octupole correlations. This observation indicates that nuclear chirality can be robust against the octupole correlations. It is of highly scientific interest to search for the chirality-parity quartet bands in nucleus with both stable triaxial and octupole deformations.     

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

Using the Bogoliubov inequality, we extend previously known results concerning the absence of continuous symmetry breakdown for equilibrium states of certain quantum and classical lattice, and continuum systems in two space dimensions.Partially supported by the N.S.F. under grant MCS 7801433.Partially supported by the N.S.F. under grant MCS 7906633.     

Spontaneous symmetry breaking of a Bose-Fermi mixture in a two-dimensional double-well potential

We study the spontaneous symmetry breaking of a superfluid Bose-Fermi mixture in a two-dimensional double- well potential. The mixture is described by a set of coupled Gross-Pitaevskii equations. The symmetry breaking phenomenon is demonstrated in the two-dimensional double-well potential in the mixture. The results are summarized in the phase diagrams of the mixture particle numbers, which are divided into symmetric and asymmetric regions by the asymmetry ratios. The dynamical pictures of the spontaneous symmetry breaking induced by a gradual transformation of the single-well potential into a double-well one are also illustrated. The properties of the quantum degenerate mixture are explored using the realistic parameters for a 40 K- 87 Rb system.     

Renormalization Conditions and the Sliding Scale in the Implicit Regularization Scheme: A Simple Connection

We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the calculation, the introduction of a mass scale is a direct consequence of a set of renormalization conditions. As an illustration the one-loop -function for QED and ⁴ theories are derived. They are given in terms of derivatives of appropriately systematized functions (related to definite parts of the amplitudes) with respect to a mass scale . Our formal scheme can be easily generalized for higher loop calculations.     

Spontaneous symmetry breaking of a Boseben Fermi mixture in a two-dimensional double-well potential

We study the spontaneous symmetry breaking of a superfluid Bose-Fermi mixture in a two-dimensional double-well potential. The mixture is described by a set of coupled Gross-Pitaevskii equations. The symmetry breaking phenomenon is demonstrated in the two-dimensional double-well potential in the mixture. The results are summarized in the phase diagrams of the mixture particle numbers, which are divided into symmetric and asymmetric regions by the asymmetry ratios. The dynamical pictures of the spontaneous symmetry breaking induced by a gradual transformation of the single-well potential into a double-well one are also illustrated. The properties of the quantum degenerate mixture are explored using the realistic parameters for a ⁴⁰K-⁸⁷Rb system.     

New Electroweak Model Without a Higgs Particle

A new unified electroweak model is proposed in this paper. In this unified electroweak model, Higgsmechanism is not used, so no Higgs particle exists in the model. In order to keep the masses of intermediate gaugebosons non-zero, two sets of gauge fields will be introduced. In order to introduce symmetry breaking and to help tointroduce the masses of all fields, a vacuum potential is needed. Except for those terms concerning Higgs particle, thefundamental dynamical properties of this model are similar to those of the standard model. And in a proper limit, thismodel will approximately return to the standard model. The purpose of this paper is not to say that the Higgs particledoes not exist in Nature, it is only to prove that, without a Higgs particle, we can also set up a unified electroweak modelwhich is consistent with present experiments.     

QGP有效微扰论中纯规范场的二圈热力学势

使用基于硬热圈(HTL)的重求和方法,计算了QGP中纯规范场的二圈热力学势及其重整化,得到了包含集体效应的结果.     

Symmetry breaking in the opinion dynamics of a multi-group project organization

A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group’s opinion evolution is driven by two types of forces:(i) the group’s cohesive force which tends to restore the opinion back towards the initial status because of its company culture;and(ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness.Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes,i.e.,a deadlock regime,a convergence regime,and a bifurcation regime in opinion dynamics.The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to.In the case of a three-group project with a symmetric social network,both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord,instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay’s result(Physica A 378(2007) p.125 Fig.5),project organization(PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations,which urges that apart from divergence in participants’ interests,nonlinear interaction can also make conflict inevitable in the PO.The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO.It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.     

光子—声子相互作用模型的基态特性研究

采用新的相干态波函数的方法,对简单的光子－声子相互作用模型的基态特性进行了研究,非常简单地导出了模型的精确基态能与基态波函数,并且对其物理意义进行了讨论。     

Improved mean field analysis of spontaneous symmetry breaking in a bidirectional two-lane system with narrow entrances

This Letter presents an improved mean field analysis of a bidirectional two-lane asymmetric exclusion process with narrow entrances, which exhibits spontaneous symmetry breaking. The method takes into account the correlation of the vertical cluster at system boundaries, which shows better agreement with simulations than the simple mean field method.     

迭代正则化方法求解电介质中空间电荷分布

首先介绍了迭代正则化方法的理论基础,建立了含有空间电荷密度分布的Fredholm第一类积分方程的反卷积算法,利用数值实验研究了加性高斯白噪声对迭代反卷积算法的影响,以及迭代停止标准对非适定问题的数值解的影响,最后使用该方法求解电介质样品中的空间电荷分布.结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出非适定问题的解.当噪声影响增大,信噪比降低时,反卷积的计算结果受到明显的影响.迭代停止标准对数值解的计算精度起着明显的作用.对实际测量数据进行处理表明,迭代正则化反卷积算法能够计算出固体电介质中的空间电荷分布.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.     

同伦正则化算法求解多宗量瞬态热传导反问题

以Bregman距离函数作为正则化泛函,建立了多宗量瞬态热传导反演的一种求解模式,可对导热系数和边界条件等进行联合识别.时域上采用精细算法进行离散,并应用同伦算法进行求解.对信息的测量误差和初值选取作了初步探讨,并进行了数值验证.