Renormalized finite temperature effective potential ofSU(2) Yang-Mills theory

It is shown that the renormalized finite temperature effective potential for continuumSU(2) Yang-Mills theory develops a non-perturbative minimum for sufficiently strong coupling, i.e. below a critical temperature. The corresponding phase can be the candidate for the confining phase of the continuum theory and becomes energetically favoured basicly due to the decay of theA ⁰ condensate into three gluons.     

Renormalized Polyakov loop in the fixed scale approach

I compute the deconfinement order parameter for the SU(2)$\mathit{SU}(2)$ lattice gauge theory, the Polyakov loop, using the fixed scale approach for two different scales and show how one can obtain a physical, renormalized, order parameter. The generalization to other gauge theories, including quenched or full QCD, is straightforward.     

Corrections to scaling and finite size effects

Numerical investigations of critical phenomena might lead to different leading correction-to-scaling terms, depending on the type of analysis. We discuss which leading correction-to-scaling behavior is expected for finite system sizes, using two-dimensional percolation as our main example. It turns out that a finite-size scaling from length L to L - 1 is less perturbed by correction-to-scaling terms.     

非对称Anderson模型的重整微扰展开

利用Yamada微扰论结合重整微扰方法来计算非对称Anderson模型,得到了局域电子占据数、重整化因子、重整化的局域能级以及重整化参数关于裸参数的展开式.计算了局域电子态密度和低温杂质电导,还计算了磁场对它们的影响,这些结果适用于从弱耦合到强耦合的整个耦合强度区域.由于在哈密顿量中已经将局域能级进行了初步重整,采用的重整微扰方法比Hewson的重整微扰方法更适合于研究非对称Anderson模型. 关键词： 非对称Anderson模型 重整化 磁场     

Renormalized transport equations for the bistable potential model

Renormalized transport equations for general Fokker-Planck systems are derived and applied to the bistable potential model. The exact equation for the expectation value x _t can be evaluated in both domains Dx _± and xD ₀ outside and between the potential minima, leading to drastic differences of the dynamics prevailing inD _± andD ₀, respectively.     

Antisymmetrization effects on the effective internuclear potential

The effects of internuclear antisymmetrization in nucleus-nucleus scattering are studied by examining the structure of the exchange-Hamiltonian kernel function in the resonating group formulation. By investigating the features of the effective local potentials which are constructed to yield the same Born scattering amplitudes as the various nucleon-exchange terms in this kernel function, it is found that, among all exchange terms, the one-exchange and core-exchange terms have the largest influence. In addition, this investigation shows that the one-exchange terms, giving rise to a Wigner-type effective potential, are generally important in all scattering systems and over a wide energy range, while the core-exchange terms, giving rise to a Majorana-type effective potential, are generally important only when the nucleon-number difference of the interacting nuclei is rather small. Based on these results, it can therefore be concluded that, if a local-potential model is adopted to analyze experimental scattering results, then the real central part of the effective potential in this model must, in general, contain a Majorana exchange component or an odd-even l-dependence. Explicit resonating-group calculations in ${}^3\text{He}\text{+ α}\text{and}\text{α +}{}^{16}\text{O}$ systems, where contributions from individual exchange terms are studied, have also been performed. From this study, one finds that the conclusions mentioned above, reached in the Born approximation, may in fact be valid even in the lower-energy region.     

The size of finite size effects in lattice gauge theories

If a quantum field is enclosed in a spatial box of finite volume, its mass spectrum depends on the box size L. For field theories in the continuum Lüscher has shown to all orders in perturbation theory that for large L this dependence is related to certain scattering amplitudes of the infinite volume theory. We derived the corresponding relations for lattice field theories. Assuming their validity for lattice gauge theory outside the perturbative region the magnitude of finite size effects on the spectrum is determined by a glueball coupling constant. This quantity is estimated by strong coupling methods.     

Twist and finite size effects for the source method

We analyze the finite size effects for the source method in pure lattice gauge theory at weak coupling. They are found to be strongly suppressed by twisting the boundary conditions, forSU(3) by typically an order of magnitude.     

Auxiliary field loop expansion of the effective action for a class of stochastic partial differential equations

We present an alternative to the perturbative (in coupling constant) diagrammatic approach for studying stochastic dynamics of a class of reaction diffusion systems. Our approach is based on an auxiliary field loop expansion for the path integral representation for the generating functional of the noise induced correlation functions of the fields describing these systems. The systems we consider include Langevin systems describable by the set of self interacting classical fields ?_i(x,t)${?}_i(x,t)$ in the presence of external noise η_i(x,t)${\eta }_i(x,t)$, namely (∂_t−ν∇²)?−F[?]=η$({\partial }_t-\nu {\nabla }^2)?-F\left[?\right]=\eta$, as well as chemical reaction annihilation processes obtained by applying the many-body approach of Doi–Peliti to the Master Equation formulation of these problems. We consider two different effective actions, one based on the Onsager–Machlup (OM) approach, and the other due to Janssen–deGenneris based on the Martin–Siggia–Rose (MSR) response function approach. For the simple models we consider, we determine an analytic expression for the Energy landscape (effective potential) in both formalisms and show how to obtain the more physical effective potential of the Onsager–Machlup approach from the MSR effective potential in leading order in the auxiliary field loop expansion. For the KPZ equation we find that our approximation, which is non-perturbative and obeys broken symmetry Ward identities, does not lead to the appearance of a fluctuation induced symmetry breakdown. This contradicts the results of earlier studies.     

去趋势波动分析方法中不重叠等长度子区间长度的确定

针对去趋势波动分析方法中参数不重叠等长度子区间长度s的选取,基于信息论的基本原理,提出使用符号分析方法对原始数据进行符号编码,并使用不同的方式对符号序列进行分段、计算互信息函数.细致描述了不同分段方式对原始混沌序列的信息编码能力,以此判断所采用的分段方式能否真实有效地还原原始序列所包含的全部信息.给出了确定最优分段个数或各分段长度的具体方式,确定了不重叠等长度子区间长度s的选取算法,以及判断所研究序列是否适用于去趋势波动分析方法,避免了以往参数s选取中随机性和主观性给计算结果带来的错误信息.进一步将该方法应用于实际温度资料,计算并分析中国1961—2000年逐日平均温度的去趋势波动分析指数分布状况.     

Optimized Rayleigh–Schrödinger expansion of the effective potential

An optimized Rayleigh–Schrödinger expansion scheme of solving the functional Schrödinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the λφ⁴ field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism.     

Effective classical potential for fluctuating field systems of finite size

We extend a previously proposed variational method in which quantum mechanical path integrals over fluctuating orbits are approximated by single integrals over an effective classical potential, to field systems of finite size and point the way for higher order corrections.     

拓扑绝缘体薄膜和有限尺寸效应

拓扑绝缘体是近年来发现的一类新的量子材料,已成为凝聚态物理的研究热点领域.厚度仅几纳米的拓扑绝缘体薄膜不但具有奇特的物理性质,而且还是拓扑绝缘体应用于平面器件的基础.文章以Bi2Se3为例,介绍了Bi2Se3家族拓扑绝缘体薄膜的分子束外延生长以及其能带、自旋结构和拓扑性质随层厚的演化.这些结果为人工调控拓扑绝缘体的电子结构和物理性质提供了指导.     

Cut-offs and finite size effects in scale-free networks

We analyze the degree distributions cut-off in finite size scale-free networks. We show that the cut-off behavior with the number of vertices N is ruled by the topological constraints induced by the connectivity structure of the network. Even in the simple case of uncorrelated networks, we obtain an expression of the structural cut-off that is smaller than the natural cut-off obtained by means of extremal theory arguments. The obtained results are explicitly applied in the case of the configuration model to recover the size scaling of tadpoles and multiple edges.Received: 18 November 2003, Published online: 24 February 2004PACS: 89.75.-k Complex systems - 87.23.Ge Dynamics of social systems - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

An effective analytical potential including plasma effects

In this work, we have developed a method to build an effective analytical potential for ions in slightly nonideal plasmas. This proposed potential is obtained from an analytical isolated potential with one or two parameters depending on the total number of electrons of the ion. The plasma effects are included by means of the linearized Debye-Hückel approximation taking into account the reaction of the plasma-charge density to the optical electron. Due to the influence of the plasma over the atomic potential, this permits to obtain level energies and wave functions as a function of the inverse of Debye radius, the quantum numbers, the nuclear charge, the bound electron number and the ionization state of the ion. Also, we compare the analytical effective potential proposed in this paper with other ones very well known in the available literature.