Variational Cumulant Expansion Study of Z(N) Lattice Gauge Theory with Symanzik's Improved Action

With the variational cumulant expansion (VCE) method, the internal energy and the specific heat of the Z(N) lattice gauge theory with Symanzik's improved action are calculated up to the third order. The variational parameter is determined by the main valued method and the result is compared with the VCE result for standard Wilson action. Furthermore, the changes are compared with those of the SU(2) case.     

基于三阶累积量的自适应多变量相空间重构

利用三阶累积量反映多变量序列的高阶非线性相关性,建立了一种具有良好抗噪性的多变量相空间重构方法.将三阶累积量引入到序列局部本征维数(LID)的计算中,对不同相空间点构造新的三阶累积量相关矩阵;同时建立累积量切片评价函数,通过比较得到了对噪声及嵌入维数等重构参数变化鲁棒性强的累积量切片,然后确定序列的嵌入维数、嵌入延迟,重构多元变量相空间.仿真结果表明,建立的新方法对带噪声混沌序列具有较好的鲁棒性,多元变量奇异吸引子轨迹在重构相空间中得到了良好扩展.
     

高能核-核碰撞中矩的振荡现象

引入密度函数与多重数分布的矩的定义,推广ｅ＾＋ｅ＾－和ｐｐ作用中的矩分析到核作用中,分析相对论核－核碰撞的ＥＭＵ０１实验数据,计算了产生的带电粒子多重数分布的Ｈｑ值,系统研究了Ｈｑ对入射能量,射弹与靶核质量、赝快度区域以及碰撞中心度的依赖关系,比较和分析了简单与复杂碰撞系统的振荡结构以及可能的物理起源。     

量子Heisenberg模型的变分累积展开研究

发展了变分累积分展开方法,并用于处理量子Ｈｅｉｓｅｎｂｅｒｇ模型,显示从自由能的解析性质出发,原则上能确定系统的临界温度到任意精确的级次;给出了产方格点上自旋１／２体系达到三次累积展开的临界温度,并与存在结果作了比较。     

An Analytical Study of Three-State Potts Model on Lattice

We investigate the phase structure of the three-state Potts model by the variational cumulant expansion approach. It is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.     

Analysis of a nonlinear stochastic model of cooperative behaviour

A stochastic model of cooperative behaviour is analyzed with regard to its critical properties. A cumulant expansion to fourth order is used to truncate the infinite set of coupled evolution equations for the moments. Linear stability analysis is performed around all the permissible steady states. The method is shown to be incapable of reproducing the critical boundary and the nature of the phase transition. A linearization, which respects the symmetry of the potential, is proposed which reproduces all the basic features associated with the model. The dynamics predicted by this approximation is shown to agree well with the Monte-Carlo simulation of the nonlinear Langevin equation.     

Quantum shot noise: Expansions in powers of the pulse density

Quantum shot noise consists of individual pulses which contribute time-dependent (operator) potentials toward a total potentialV(t). The averaged quantity T exp _t0 ^t dtV(t) in general can no longer be calculated explicitly, in contrast to the classical case, and expansions are of interest. Noncommutative cumulant expansions are not directly applicable if the correlation functions ofV(t) have singularities, as happens in applications. It is shown here that these expansions, when applied to quantum shot noise, can be partially summed to give expansions in powers of the pulse density. Three types of such expansions are established explicitly, and for two of them the derivation is direct. For one of them the first-order approximation is closely connected to the so-called unified theory of spectral-line broadening.     

用变分累积展开方法计算磁性薄膜的临界指数γ(L)与β(L)

Ｌｉｎ Ｄｏｕｌｉａｎｇ等人把变分累积开展（ＶＣＥ）方法用于薄膜，计算了各种结构的磁性薄膜的临界温度。本文是文献〔１〕的继续，计算了Ｌ层磁性薄膜的临界指数γ（Ｌ）与β（Ｌ），计算结果一文献〔３￣５〕的实验结果符合。对于Ｌ＝１（相当于２维）这一特征，我们的计算结果与精确解符合得相当好。     

基于高阶累积量的文本图像去噪算法

根据高斯噪声三阶以上累积量为零,从而可以将其有效抑制的特点,提出了一种基于高阶累计量的文本图像去噪方法.与平滑滤波和中值滤波2种经典算法相比,高阶累积量的使用不仅提高了文本图像去噪效果,而且能够较好地保留图像的边缘和细节信息,保证了原有文字的完整性.实验表明,提出的去噪算法对于去除文本图像的加性高斯噪声较为理想.     

利用高阶统计量恢复二维谐波

基于高阶统计量提出了一种频域恢复频率、时域恢复幅度的时频域相结合的二维谐波信号的恢复方法。该方法由于使用了高阶累积量，因此不再受背景噪声为高斯白噪声的限制，可应用于高斯噪声中二维谐波信号的恢复。仿真实验证明了该方法的可行性