二级相变理论和Lifshitz条件不成立的论证

系统的自由能是序参量的泛函。在二级相变点附近,自由能密度是序参量及其关联项的幂次展式。按本文给定的方法,无论关联项是定域还是非定域的,由对自由能的一级变分等于零,都能求得表示平衡态位形的序参量。在求解过程,必须将序参量进行傅氏变换,这与序参量以系统对称群的基函数展开是一致的,由此对二级相变中对称改变进行了分析。利用变分法中极值的充要条件(或充分条件),我们讨论了二级相变过程中状态的稳定性条件。由于我们对自由能求极值时没有略去关联项,因此不存在Lifshitz的对称改变限制条件。这里强调指出:实质上,Lif     

高增益自发参量下转换光的关联成像

本文研究了高增益自发参量下转换光的关联成像。在高增益自发参量下转换光束中，既存在信号光和闲置光之间的量子纠缠关联，每束光自身还满足热光统计性质，具有经典热光关联。因此可以利用高增益自发参量下转换过程同时产生两种关联成像方式：纠缠双光子关联成像和热光关联成像。本文比较了纠缠双光子关联成像和热光关联成像的异同，并详细讨论了各种成像条件下高增益自发参量光源的关联成像。     

正电子湮没参量及其所反映物质信息的探讨

本根据正电子在凝聚态物质中的湮没机制及捕获模型,讨论了正电子湮没参量——正电子寿命谱和多普勒线形等参量所反映的物质信息,给出了各正电子湮没参量与所反映的物质信息之间的定量关系。分析了在该体系中正电子寿命参量与局域电子密度、多普勒线形参量和角关联参量与电子动量密度分布和费米面之关联。     

Erd¨os R′enyi随机网络上爆炸渗流模型相变性质的数值模拟研究

基于改进的Newman和Ziff算法以及有限尺寸标度理论,通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟,分析研究了Erd¨os R′enyi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明:尽管序参量表现出了不连续相变的特征,但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erd¨os R′enyi随机网络中的爆炸渗流相变是一种奇异相变,它既不是标准的不连续相变,又与常规随机渗流表现出的连续相变处于不同的普适类.     

Erdös Rényi随机网络上爆炸渗流模型相变性质的数值模拟研究

基于改进的Newman和Ziff算法以及有限尺寸标度理论, 通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟, 分析研究了Erdös Rényi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明: 尽管序参量表现出了不连续相变的特征, 但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erdös Rényi随机网络中的爆炸渗流相变是一种奇异相变, 它既不是标准的不连续相变, 又与常规随机渗流表现出的连续相变处于不同的普适类. 关键词： Erdös Rényi随机网络 爆炸渗流模型 相变 幂律标度行为     

三体关联与次近邻两体关联下的渗流

本文用实空间重正群(RSRG)方法对二维三角格子的淬火体系,处理其在三体关联及最近邻与次近邻关联下的渗流问题。对于格点多体关联函数采用叠加近似,对于格点-空位多体关联是由几率守恒求出的。结果表明,引入三体关联或次近邻关联后,都并不改变临界现象的普适律。 关键词：     

一维扩展量子罗盘模型的拓扑序和量子相变

应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.     

量子隧道系统与两声子库关联压缩基态的变分法研究

用变分法研究了量子隧道系统与两声子库的关联压缩变换的基态能量．发现：1)对两个声子模式,在一定模型参量下,考虑关联效应后的声子基态能量比不考虑关联效应的声子基态能量更低．2)对于不同的模型参量,关联效应的影响也不同：在声子与二能态系统的共振区内,随着两个声子间的耦合度及对共振峰值的逼近,关联效应将随之增强.     

铁氧体参量耦合振荡的理论分析

在本文中我们系统地讨论了铁氧体小样品在超高频电源的激发下产生参量振璗的耦合关系,指出激发机构应分为磁场驱动和磁化驱动二类。前者的特例为Denton新近发现的,使用空间均匀的纵向注入场;后者的特例为Suhl最早所研究的,使用空间均匀的横向注入场所激发的一致进动的磁化向量为驱动力。从静磁势函数的耦合微分方程我们得到这二种特殊注入方式激发的静磁势函数的完全解(一次近似),表达为Walker函数的线性组合,在边界连续的要求下,这些势函数中的Walker模只在它们的指标之间适合一定的条件时才相互关联。当直流磁场调谐于一对Walker模时,耦合的静磁势简化为静磁操作的势函数。我们具体分析了静磁操作参量振璗从注入场吸取的功率,根据后者必须不为零才可能产生参量振璗,我们推导出空间均匀场激发一对静磁模的选择定则,恰与从边界连续推出的关联条件完全相同,并且进一步得到空间不均匀场激发一对静磁模的选择定则。我们指出,参量振璗的振幅的决定必须引用能量守恒和量子数相等的方程。最后我们采用Suhl的方法推算出空间均匀的纵向注入场的激发临阈强度,并且讨论了这一方法的近似性质。     

实用化多功能光压缩器

激光二极管抽运的YAPKTP内腔倍频单频激光器及其抽运的半整块非简并光学参量振荡腔(NOPO)被固定在一体的殷钢底座上构成了全固化多功能光压缩器———Squeezer.通过控制不同的工作条件,在此装置上可以产生多种类型压缩光:阈值以上产生约6dB(74%)量子相关孪生光束;在阈值以下,通过注入信号光参量缩小过程产生21dB明亮正交振幅压缩光;将参量放大器出射的两个频率简并偏振垂直的孪生光束分开,获得振幅反关联位相正关联明亮EPR源. 关键词： 光压缩器 光学参量振荡腔(OPO) 全固化     

Correlated percolation — a real-space renormalization group study

A quenched-correlated percolation system is studied by using the real-space renormalization group method. We chose the nearest-neighbour short-range order α as the correlation parameter. By treating the correlated probability self-consistently in terms of site occupation probability p and α, we found that, in two dimensions, there is only one nontrivial physical fixed point at random percolation and the correlation is an irrelevant parameter which always leads to the same universality.     

High-field vs. low-field magneto-transport in a percolating medium

Recent theoretical and numerical work on high-field magneto-transport in a percolating medium is described and compared to earlier work on weak-field magneto-transport in such systems. While the weak-field behavior is well described by the simple nodes-links picture, which ignores blobs and loops on a scale smaller than the percolation correlation length ξ_p, the strong-field behavior is extremely sensitive to those features. The critical behavior at strong magnetic fields H near the percolation threshold is governed by competition between the usual H=0 fixed point and a new H=∞ fixed point. Which of those fixed points dominates the behavior is determined by the relative sizes of two characteristic lenghts: the percolation correlation length ξ_p and a new, magnetic field dependent length ξ_H.     

Two—phase flow in correlated pore—throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and ε. The E～ L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.     

Collapse of percolation clusters — A transfer matrix study

Exact calculations using transfer matrices on finite strips are performed to study the two-dimensional problem of site percolation clusters with an attractive nearest neighbor interaction. Thermodynamic quantities such as free energy per site and specific heat are calculated. Finite-size scaling with two strips of different widths yields very accurate approximations of the critical line and the correlation length exponent. The result shows clearly a site percolation fixed point at very high temperatures, a random animal fixed point at intermediate temperatures, a point for the collapse of lattice animals at lower temperatures, and a compact-cluster fixed point at the lowest temperatures.On leave from Institute of Theoretical Physcis, Chinese Academy of Sciences, Beijing, China.     

A damage model based on failure threshold weakening

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long-range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size L is increased for fixed R. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.     

A finite fractal cluster theory of 1/f noise in percolation systems near metal-insulator transition

The problem of 1/f noise in thin metal films and metal-insulator composites in the scaling fractal regime near percolation threshold is considered. The correspondence between a percolation transition and a second order phase transition is extended from the point of view of electronic polarization and electrical fluctuations. The charge fluctuations on finite fractal clusters are argued to be analogous to spontaneous order parameter fluctuations in phase transitions, being correlated upto percolation correlation length. The charge relaxation times are shown to be related to the cluster sizes having distribution function of the formg()^–b , whereb is connected to Euclidean and fractal dimensionalities and critical exponents. This produces the 1/f noise spectrum. Below percolation threshold, the nodes-links-blobs picture is invoked such that the blobs represent metallic conductances of the finite clusters and the links are tunnelling conductances between them through narrowest barrier regions. Above threshold, the finite cluster network is visualized as connected to the infinite cluster through narrowest tunnelling regions. The correlated spontaneous charge fluctuation on finite fractal clusters is held responsible for conductance fluctuation on either side of the metal-insulator transition via tunnelling processes. Finally, the scaling behaviour of noise magnitude near percolation threshold is explained.     

Percolation transport in random flows with weak dissipation effects

In the present paper, we consider the influence of weak dissipative effects on the passive scalar behavior in the framework of continuum percolation approach. The renormalization method of a small parameter in continuum percolation models is reviewed. It is shown that there is a characteristic velocity scale, which corresponds to the dissipative process. The modification of the renormalization condition of the small percolation parameter is suggested in accordance with additional external influences superimposed on the system. In the framework of mean-field arguments, the balance of correlation scales is considered. This gives the characteristic time that corresponds to the percolation regime. The expression for the effective coefficient of diffusion is obtained.     

Tricritical point in explosive percolation

The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With high-precision simulations of the order parameter and the second moment of the cluster size distribution a fully consistent tricritical scaling scenario emerges yielding the tricritical crossover exponent 1/φ(t)=1.8 ± 0.1.     

Scale invariance in percolation theory and fractals

The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot transformation, leading to a fractal behavior of the percolation probability in the complex plane. The hierarchical chains of impedances, reducing to a nonlinear mapping of the impedance space onto itself, are studied. An infinite continuation of the procedure leads to a fixed point. It is shown that the number of steps required to reach a neighborhood of this point has a fractal distribution. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 427–432 (25 September 1996)     

基于节点相关性的网络不动点理论研究

现代复杂的通信网络内部存在着广泛的幂律现象，网络节点之间存在相关特性. 根据这种相关特性，提出了网络不动点理论. 将Banach不动点理论引入网络模型，证明了网络不动点理论的正确有效性. 证明过程是把通信网络看作由路径预测算法产生的似马尔可夫链的路由节点迭代序列形成的网络空间. 由节点相关性可知，此空间中的节点序列相对越长就越能折射出搜索的目标所在，预测准确率也会逐步增加，可以更好地进行目标定位、数据挖掘等. 通过某种路由准则的算子从源节点最终映射到的目的节点与Banach空间的不动点相对应，即为网络空间的不动点. 当网络发展到能为用户提供真正的无处不在的连接时，网络不动点理论的物理特性将非常明显. 因为网络规模越大，节点间的群体作用越显著，就越能显现网络不动点理论的物理特性. 关键词： 计算机网络 长程相关 不动点 幂律