关于海森堡模型中一种并行算法实现的讨论

使用并行算法(简称Z分法)Fortran编程计算获取海森堡模型位型[N,k](N为海森堡链总格点数,κ为格点中自旋向上的电子数)最小本征值的最短时间、使用置换群方法产生模型的能量矩阵,将能量矩阵对角化所得到的本征值构成数据群,采用Z(Z=1,2…)分法Fortran编程计算获得群中最小数据的最短(或最长)时间。结果表明:同一位型[N,k],使用2分法获取模型位型[N,k]最小本征值的时间最长,而不等分或满等分(此时Z=1或位型[N,k]的矩阵维数)时的时间最短且二者相等;对于不同位型[N,k]当N(k)同,k(N)增大且Z相同时,获取模型最小本征值的最短时间增加。     

海森堡模型中概率及相应熵的计算分析

介绍海森堡模型的不同位型[N,n] （N为海森堡链总格点数, n为格点中自旋向下的电子数）中的体现本征值获取难易程度的本征值获取概率及其相应信息熵（香农所定义的）和体现模型体系关联程度的自旋向下电子发现概率、每一粒子的von Neumann及体系的平均von Neumann熵,可为量子计算与信息传递提供启示性信息。研究结果：(1)事件发生概率大于（小于）50%时,信息熵随概率增加而减小（增加）。(2)不同位型[N,n],当n（N）同, N（n）增加时：本征值获取概率减小,其相应的信息熵正确反映本征值获取的难易程度;模型参数一定时,格点中自旋向下电子发现概率与每一粒子的von Neumann及体系的平均von Neumann熵都分别减小（增加）。(3)位型[N,n]相同时, 每一粒子的von Neumann及体系的平均von Neumann熵随参数变化时出现拐点,显示体系发生量子相变的信息。(4)同位型[N,n]且同参数时处于海森堡链对称位置粒子的von Neumann熵相同。     

一维XY海森堡模型纠缠度的计算与相关分析

计算了一维XY海森堡模型的基态纠缠度并作相关分析,为量子通信和量子计算提供启示性信息.将von Neumann熵定义的纠缠度与模型的基态本征矢建立联系计算出该模型体系的基态纠缠度.计算结果表明,(1)总格点数N相同,自旋向上电子数k增加时,基态纠缠度η增加;k相同,N增加时,η减小,真实反映了此模型的关联性.(2)N为偶数,位型[N,N/2]时,η=1,体现了自旋链格点中自旋向上和向下的电子数呈严格的对称性.(3)模型参数不同, η有別.(4)η在整个参数变化区间内的导率一致,体系为有纠缠的连续长程相,属于从有序到有序的相变.     

一维XY每森堡模型纠缠度的计算与相关分析

计算了一维XY 海森堡模型的基态纠缠度并作相关分析,为量子通信和量子计算提供启示性信息。将von Neumann 饷定义的纠缠度与模型的基态本征矢建立联系计算出该模型体系的基态纠缠度。计算结果表明(1) 总格点数N 相同,自旋向上电子数k 增加时,基态纠缠度η 增加k 相同N 增加时T) 减小,真实反映了此模型的关联性。(2) N 为偶数,位型[N, N/2] 时, η= 1 ,体现了自旋链格点中自旋向上和向下的电子数呈严格的对称性。(3) 模型参数不同, η 有别。但)η 在整个参数变化区间内的导率一致,体系为有纠缠的连续长程相,属于从有序到有序的相变。     

一维海森堡链格点中不同电子自旋交换构成能量矩阵的方法

对一维海森堡链格点中不同电子自旋交换如何构成及所构成的能量矩阵进行讨论,为纠缠度和量子计算提供重要依据.研究方法是:一维海森堡链格点被电子填充分为单、双占据及二者共存三种情况.相邻格点中电子自旋交换分两类,第Ⅰ类:相邻格点最相邻电子自旋交换;第Ⅱ类:"间隔"交换,分为"左间隔"与"右间隔"两种交换(即格点左(右)侧电子与相邻格点左(右)侧电子自旋之间的交换).将一维海森堡体系的哈密顿算符作用于完备基矢(用置换群所构建)形成能量矩阵.计算结果: (1)位型[4,2]的第Ⅰ类自旋交换在格点单、双占据及格点单、双占据共存三种情况时所得矩阵只在对称填充时相同,别况均不同. (2)位型[4,2]在格点双占据的第Ⅱ类与第Ⅰ类自旋交换所形成的矩阵只在格点被对称填充时相同,别况均不同;自旋"左间隔"交换与"右间隔"交换时,同样哈密顿算符作用于同样完备基矢所得矩阵有些相同,有些不同.最后说明所计算的不同位型矩阵的规律及研究意义.     

利用MATLAB和行列式计算超晶格束缚态能量本征值的一种简捷方法

在计算超晶格束缚态能量本征值时,根据势阱与势垒界面的连续性条件,将界面两侧的波函数展开为一个以矩阵方 程描述的线性方程组,再根据束缚态的能量本征值必须满足该方程组的系数行列式等于零的要求,在能量区间内进行逐点扫描,并利用MATLAB矩阵 行列式计算函数,即可确定相应的能量本征值。与递推法、转移矩阵法等其他方法相比,该方法不需要花费较多的精力来编程,具有概念简 单、使用方便、实用性强等特点。     

用具有伪频率消除的共轭梯度法进行自适应频谱估计

在Ｐｉｓａｒｅｎｋｏ方法中，谱线的信息包含在与数据协方差矩阵的最小本征值相对应的木征矢量中。本文采用共轭梯度法自适应地求出与最新信号协方差矩阵的最小本征值对应的本征矢量。然而，当所选择的系统模型的阶数明显高于实际信号模型的阶数时，会产生伪谱线。但是，只要将共轭梯度法加以改进便可以除去这些伪频率。这是通过将不希望出现的光谱零值从单位圆上找推移至复平面中，从而消除伪谱峰来实现的．因而，当所选择的系统模型的阶数与准确的系统阶数相比大许多时，具有伪频率消除的共轭梯度法可认为是消除伪谱峰较合适的方法。     

双模腔场中两Λ型三能级原子的纠缠演化

研究了2个纠缠的Λ型三能级原子与双模量子腔场的喇曼耦合模型,利用部分转置矩阵负本征值的方法,计算了两原子纠缠随时间的演化.结果表明:两原子纠缠演化呈现周期性,并且演化规律受到两原子初始状态、腔模初始光子数的影响;对于特殊的原子初态,两原子会一直处于最大纠缠而与光场初始光子数无关;与Tavis-Cummings模型相比,本模型中两原子的纠缠可以保持更长时间.     

凌力尔特推出同步降压型DC／DC开关稳压控制器LTC3775

凌力尔特公司（Linear Teehnology Corporation）推出低的最小接通时间、宽输入电压范围、同步降压型DC／DC开关稳压控制器LTC3775,该器件可驱动所有N沟道功率MOSFET级。LTC3775具有不到30ns的最短接通时间,非常适用于高降压比应用。其4．5V至38V的输入范围可涵盖多种应用．包括大多数中间总线电压和电池化学组成。     

扭转椭圆双折射光纤的非扭转等效

由光纤长度、双折射参数和扭转速率表达的扭转椭圆双折射光纤Jones矩阵和Mueller矩阵,求得其本征值和本征矢,并和椭圆延迟器的Jones矩阵、Mueller矩阵、本征值和本征矢比较,从而说明扭转椭圆双折射光纤可以和等长度的无扭转椭圆双折射光纤等效.两种矩阵表达式下求出的等效椭圆双折射参数相同,据此对等效性进行了深入讨论.     

Inferring the eigenvalues of covariance matrices from limited,noisy data

The eigenvalue spectrum of covariance matrices is of central importance to a number of data analysis techniques. Usually, the sample covariance matrix is constructed from a limited number of noisy samples. We describe a method of inferring the true eigenvalue spectrum from the sample spectrum. Results of Silverstein (1986), which characterize the eigenvalue spectrum of the noise covariance matrix, and inequalities between the eigenvalues of Hermitian matrices are used to infer probability densities for the eigenvalues of the noise-free covariance matrix, using Bayesian inference. Posterior densities for each eigenvalue are obtained, which yield error estimates. The evidence framework gives estimates of the noise variance and permits model order selection by estimating the rank of the covariance matrix. The method is illustrated with numerical examples     

基于张量分解的双基地MIMO 雷达目标数估计

针对双基地多输入多输出(MIMO)雷达目标数估计问题,提出一种基于三阶张量分解的目标数估计算法。该算法首先将匹配滤波输出转化为三阶张量;然后,从张量的三个维度分别计算特征值,并通过迭代方法估计全局特征值;最后,利用全局特征值估计目标数。与传统基于矩阵分解算法相比,该算法充分利用了回波数据的多维结构特征,可有效改善特征值的估计精度,从而提高目标数的正确估计概率。仿真结果证明了所提算法的有效性和优越性。     

Optimal Linear Coding for Vector Channels

This paper is concerned with the problem of obtaining the optimal linear vector coding (transformation) method that matches anr-dimensional vector signal and ak-dimensional channel under a given channel power constraint and mean-squared-error criterion. The encoder converts thercorrelated random variables intorindependent random variables and selects at mostkindependent random variables which correspond to theklargest eigenvaiues of the signal covariance matrixQ. The encoder reinserts cross correlation into thekrandom variables in such a way that the largest eigenvalue ofQis assigned to the smallest eigenvalue of the channel noise covariance matrixRand the second largest eigenvalue ofQto the second smallest eigenvalue ofR, etc. When only the total power for allkchannels is prescribed, the optimal individual channel power assignments are obtained in terms of the total power, the eigenvalues ofQ, and the eigenvalues ofR. When the individual channel power limits are constrained byP_{1}, ..., P_{k}andRis a diagonal matrix, the necessary conditions of an inverse eigenvalue problem must be satisfied to optimize the vector signal transmission system. An iterative numerical method has been developed for the case of correlated channel noise.     

基于随机矩阵非渐近谱理论的协作频谱感知算法研究

将随机矩阵的非渐近谱理论应用到协作频谱感知中,对接收信号样本协方差矩阵的最大特征值和最小特征值进行分析,该文提出一种精确的最大最小特征值差(Exact Maximum Minimum Eigenvalue Difference, EMMED)的协作感知算法。对于任意给定的协作用户个数K和采样点数N,首先推导了最大最小特征值之差的精确概率密度函数(Probability Density Function, PDF)和累积分布函数(Cumulative Distribution Function, CDF),然后利用该分布函数设计了所提算法的判决阈值。理论分析表明,EMMED算法的判决阈值较已有的渐进最大最小特征值差(Asymptotic Maximum Minimum Eigenvalue Difference, AMMED)检测更为精确,算法无需主用户信号特征并且能够对抗噪声不确定度影响。仿真结果表明,存在噪声不确定度的感知环境下,EMMED算法较已有的精确最大特征值(Exact Maximum Eigenvalue, EME)和EMMER等频谱感知算法具有更好的检测性能。     

Minimum-distance bounds by graph analysis

The parity-check matrix of a linear code is used to define a bipartite code constraint (Tanner) graph in which bit nodes are connected to parity-check nodes. The connectivity properties of this graph are analyzed using both local connectivity and the eigenvalues of the associated adjacency matrix. A simple lower bound on the minimum distance of the code is expressed in terms of the two largest eigenvalues. For a more powerful bound, local properties of the subgraph corresponding to a minimum-weight word in the code are used to create an optimization problem whose solution is a lower bound on the code's minimum distance. Linear programming gives one bound. The technique is illustrated by applying it to sparse block codes with parameters [7,3,4] and [42,23,6]     

Covariance matrix properties and multiple symbol/soft decisiondetection in slow flat Rician fading

For a small number of symbols N and slow flat fading channels, it is shown that covariance matrices encountered in practice have two nonnegligible eigenvalues, the first much larger than the second, with a symmetric eigenvector associated with the first eigenvalue, and a skew symmetric eigenvector associated with the second eigenvalue. The first eigenvector is well approximated by a conditional mean, and the second eigenvector represents a small drift about the mean. The eigenvalues and eigenvectors of the slow flat fading channel covariance matrix are shown to be strongly related to those of a certain conditional covariance matrix. The maximum likelihood (ML) rules for block hard decision and symbol-by-symbol hard decision, and a rule for soft decision detection of M-DPSK, all using multiple symbol information, are obtained for the Rician channel as a function of N. The eigenvalue-eigenvector results lead to practical implementations of all rules. For small to moderate N, it is shown that a simple open-loop algorithm, of complexity N log N, attains the performance of the ML decision rules for an E_s/N ₀ range of interest for several land mobile satellite systems. The ML decision rules are seen to give rapidly diminishing returns as N increases, showing that simple noncoherent techniques can have very effective performance for the Rician fading channel. Lastly, several conclusions are drawn about the asymptotic channel behavior, including the Rayleigh channel. The work is directly applicable to the Australian and North American land mobile satellite systems     

On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks

We develop on-line routing and wavelength assignment (RWA) algorithms for WDM bidirectional ring and torus networks with N nodes. The algorithms dynamically support all k-allowable traffic matrices, where k denotes an arbitrary integer vector [k/sub 1/, k/sub 2/,... k/sub N/], and node i, 1 /spl les/ i /spl les/ N, can transmit at most k/sub i/ wavelengths and receive at most k/sub i/ wavelengths. Both algorithms support the changing traffic in a rearrangeably nonblocking fashion. Our first algorithm, for a bidirectional ring, uses [(/spl Sigma//sub i=1//sup N/ k/sub i/)/3] wavelengths in each fiber and requires at most three lightpath rearrangements per new session request regardless of the number of nodes N and the amount of traffic k. When all the k/sub i/'s are equal to k, the algorithm uses [kN/3] wavelengths, which is known to be the minimum for any off-line rearrangeably nonblocking algorithm. Our second algorithm, for a torus topology, is an extension of a known off-line algorithm for the special case with all the k/sub i/'s equal to k. For an R /spl times/ C torus network with R /spl ges/ C nodes, our on-line algorithm uses [kR/2] wavelengths in each fiber, which is the same as in the off-line algorithm, and is at most two times a lower bound obtained by assuming full wavelength conversion at all nodes. In addition, the on-line algorithm requires at most C - 1 lightpath rearrangements per new session request regardless of the amount of traffic k. Finally, each RWA update requires solving a bipartite matching problem whose time complexity is only O (R), which is much smaller than the time complexity O(kCR/sup 2/) of the bipartite matching problem for an off-line algorithm.     

Efficient evaluation of the [Z] matrix with method of moment in grounding analysis by using adaptive spatial sampling approach

The design of grounding system often relies on the performance simulations. The evaluation of the current distribution of grounding system for many frequencies by using the method of moments (MoM) may take a long time since the impedance matrix must be recomputed at each new frequency. A multiobject adaptive spatial sampling approach is presented to construct the fitted model of the electric field intensity generated by a horizontal electric dipole. The [Z] matrix spatial interpolation technology with MoM is described to reduce the computational time needed for the transient characteristics analysis of a horizontal grounding system. The accuracy and computational time of the [Z] matrix interpolation method are compared with those of the direct MoM. The numerical examples show that the [Z] matrix spatial interpolation method can reduce the computation requirement effectively.     

基于极化联合特征值的雷达弱小目标检测方法

针对海杂波背景下雷达弱小目标检测问题,提出了一种基于极化联合特征值的雷达弱小目标检测方法。该方法利用多极化通道回波数据计算极化相干矩阵的最大特征值,然后将待检测单元的最大特征值与参考单元最大特征值、最小特征值、算数平均值和几何平均值的算数平均之比分别作为检验统计量实现检验判决。仿真和实测数据处理结果表明：基于极化联合特征值的雷达弱小目标检测方法较基于特征值的检测方法性能提高2 dB,较极化检测最优滤波器性能提高1.5 dB,较功率最大综合检测方法、SPAN检测方法性能提高5 dB,极化联合最大特征值-几何平均方法综合检测效果最好。     

Efficient wide-band evaluation of mobile communications antennasusing [Z] or [Y] matrix interpolation with the method of moments

The development of novel antennas for mobile communications often relies on performance simulations. The evaluation of the antenna surface currents for many frequencies using the method of moments (MoM) can take a long time since the impedance matrix must be computed for each new frequency. This paper investigates and compares two efficient methods for the computation of the broad-band performance of mobile communications antennas using frequency interpolation of either the MoM impedance matrix [Z] or admittance matrix [Y]. In either method, the elements of only a few matrices at relatively large frequency intervals are directly computed. These matrices are then used to interpolate the elements of the respective [Z] or [Y] matrices at the intermediate frequencies. Both methods reduce the time it takes to compute the antenna performance over a wide frequency band. The implementation of each method to evaluate the performance of several different antennas used for mobile communications is discussed. Examples with both frequency-domain and time-domain results are presented and both near-field and far-field quantities are considered. The accuracy, the simulation run times, and the computational requirements of direct MoM, [Z] matrix interpolation, and [Y] matrix interpolation are compared