Coulomb interaction symmetries and the Mayer series in the two-dimensional dipole gas

We study the Mayer series of the two-dimensional dipole gas in the high-temperature, low-density regime. Without performing any multiscale analysis, we obtain bounds showing that the Mayer coefficients are finite in the thermodynamic limit. These bounds are obtained by exploiting a particular partial symmetry of the interaction (which we nameO-symmetry), already used in some problems related to the two-dimensional Coulomb gas. By direct bounds on some Mayer graphs we also conjecture that any technique based uniquely on theO-symmetry will not be sufficient to prove analyticity of the series.     

修正屏蔽库仑势下二维尘埃等离子体的动力学和结构特性

本文考虑等离子体密度分布变化, 得到了修正屏蔽库仑势的解析解. 数值分析以及分子动力学模拟表明, 在常见实验室参数情况下, 等离子体密度分布变化引起的屏蔽库仑势修正对二维尘埃等离 子体系统的动力学和结构特性影响很小. 在极限参数情况下, 本模型的计算结果表明二维尘埃等离子体系统的扩散能力明显降低, 并且系统组态呈圆形分布. 此外, 本文还研究了实验室常见大小磁场对二维尘埃等离子体系统的影响. 关键词： 修正屏蔽库仑势 二维尘埃等离子体 分子动力学模拟     

Classical coulomb systems near a plane wall. I

The equilibrium structure of classical Coulomb systems bounded by a plane wall is studied near that wall. Several models are considered: the two-dimensional one-component plasma at a special value of the coupling constant (which makes the model exactly soluble), the two-dimensional and three-dimensional one-component and two-component plasmas in the weak-coupling limit (a Debye-Hückel type of approach is then used). Along a wall, the pair correlation functions decay only as an inverse power of the distancer, namely, asr ^–v for av-dimensional system (v=2,3). The one-body densities are also studied; the first BGY equation is used.     

Derivation of Mayer Series from Canonical Ensemble

Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid(X.Z. Wang, Phys. Rev. E66(2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.     

Delta-function expansion of Mayer function with application to virial coefficients

The Mayer cluster integrals of a fluid with smooth, repulsive interactions are expanded in orders of a well-defined softness parameter. To first but not second order in softness, all virial coefficients are given by their hard-sphere forms with an effective diameter. A closed asymptotic expression is derived for the third virial coefficient which gives excellent results for the inverse power and exponential potentials.     

On potential and field fluctuations in two-dimensional classical charged systems

We supplement a previous paper on three-dimensional systems by studying the electric potential and field fluctuations in two-dimensional Coulomb systems. The novelty in two dimensions is that the fluctuations of the potential at a point are infinite in the thermodynamic limit. However, the potential difference between two points has finite fluctuations, which resemble the ones which occur in the three-dimensional case. The field fluctuations are also rather similar in both cases. The correlations do not have a fast decay. Explicit results are obtained for a solvable model; the fluctuations of the potential are Gaussian with an infinite variance.This laboratory is associated with the Centre National de la Recherche Scientifique.     

Preparation of curved two-dimensional electron systems in InGaAs/GaAs-microtubes

We present a preparation method to realise transport measurements on evenly curved two-dimensional electron systems (2DESs). By combining the method of self-rolling strained double layers with a special lithographic procedure we are able to roll-in and contact AlGaAs/GaAs/AlGaAs quantum well structures into tubes or curved lamellas. Applying a magnetic field to such structures results in a strong modulation with changing sign of the magnetic field components perpendicular to the curved 2DES plane. Our preparation method allows transport measurements along or perpendicular to this modulation. We present and discuss our first magneto-transport measurements on such rolled 2DESs.     

Convergence of Mayer expansions

The tree graph bound of Battle and Federbush is extended and used to provide a simple criterion for the convergence of (iterated) Mayer expansions. As an application estimates on the radius of convergence of the Mayer expansion for the two-dimensional Yukawa gas (nonstable interaction) are obtained.     

Mean field theory for Coulomb systems

We study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter zero. We prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field(x) where is given by-+ 2z sinh() =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.Work partially supported by NSF Grant MCS 82-02115.     

Structure search of two-dimensional systems using CALYPSO methodology

The dimensionality of structures allows materials to be classified into zero-, one-, two-, and threedimensional systems. Two-dimensional (2D) systems have attracted a great deal of attention and typically include surfaces, interfaces, and layered materials. Due to their varied properties, 2D systems hold promise for applications such as electronics, optoelectronics, magnetronics, and valleytronics. The design of 2D systems is an area of intensive research because of the rapid development of ab initiostructure-searching methods. In this paper, we highlight recent research progress on accelerating the design of 2D systems using the CALYPSO methodology. Challenges and perspectives for future developments in 2D structure prediction methods are also presented.     

Nontrivial fixed points and screening in the hierarchical two-dimensional Coulomb gas

We show the existence and asymptotic stability of two fixed points of the renormalization group transformation for the hierarchical two-dimensional Coulomb gas in the sine-Gordon representation and temperatures slightly greater than the critical one. We prove also that the correlations at the fixed points decay as in the hierarchical massive scalar free theory, that is, asd _xy ^–4 . We argue that this is the natural definition of screening in the hierarchical approximation.     

Mayer expansions and the Hamilton-Jacobi equation

We review the derivation of Wilson's differential equation in (infinitely) many variables, which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed. We show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic. The resulting series solutions are generalizations of the Mayer expansion in statistical mechanics. The differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated Mayer expansions. Applications include the Yukawa gas in two dimensions past the=4 threshold and another derivation of some earlier results of Göpfert and Mack.     

Remarks on the independence of the free energy from crystalline boundary conditions in the two-dimensional one-component plasma

We study the two-dimensional one-component plasma. We show that given a bound on the one-particle correlation functions in the thermodynamic limit the canonical free energy is independent or free of the Dobrushin-type boundary conditions obtained by putting outside the vessel a regular configuration of fixed charges.Supported by the Deutsche Forschungsgemeinschaft (D.F.G.), Forschungsprojekt Stochastische Felder.     

Generation of transient chaos from two-dimensional systems via a switching approach

A new approach of generating transient chaos from two-dimensional(2D) continuous autonomous systems within finite time is presented.Based on an absolute-value switching law,the phenomenon of transient chaos takes place by switching between three 2D systems.Basic dynamic behavior of the systems is investigated.Numerical examples illustrate the validity of the results.     

Experimental researches on quantum transport in semiconductor two-dimensional electron systems

The author reviews contribution of Gakushuin University group to the progress of the quantum transport in semiconductor two-dimensional electron systems (2DES) for forty years from the birth of the 2DES in middle of the 1960s till the finding of temperature dependent collapse of the quantized Hall resistance in the beginning of this century.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

异构二维延迟系统的广义混沌同步

基于泛函微分方程稳定性理论,利用广义混沌同步辅助分析方法,对两个异构二维延迟系统实现了广义混沌同步.与其他广义同步方法相比较,我们所使用的方法更为简便,理论分析和数值模拟证明了设计方案的有效性.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.     

A solvable model for localized adsorption in a coulomb system

A model for an interface with localized adsorption is presented, in which the surface has a distribution of sticky adhesive sites in contact with a Coulomb fluid. Contrary to the current literature on the electrical double layer the surface charge is in dynamic equilibrium with the bulk fluid. The sum rules obeyed by the one- and two-body correlation functions are investigated. Explicit results are obtained for a solvable model, the two-dimensional one-component plasma at reduced temperature 2. The effect of the granularity of the adsorbed charge on the adsorption isotherm is discussed.     

Collective modes and dynamic structure factor of a two-dimensional electron fluid

The electrons bound to the surface of liquid dielectrics by image forces are described as a two-dimensional, classical, one-component plasma with inverse distance interactions. Exact expressions for the collective modes and the dynamic structure factor are obtained from first principles in the limit of long wavelengths. The differences and analogies with uncharged particle fluids and with the three-dimensional one-component plasma are explicitly displayed. The previously used mean-field approximation is shown not to describe weakly coupled systems and to be inadequate in the long-wavelength region.