Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

基于形态学top-hat算子的多传感器图像融合

本文根据形态学top-hat算子能够提取图像中极大值与极小值区域的特点,将其应用于多传感器图像融合的两个重要领域——多聚焦图像融合和高分辨、多光谱图像融合.实验中将本文方法与Laplacian塔型变换、子波变换、主分量分析等方法进行了比较,结果表明本文所提的基于top-hat算子的融合方法具有优越的性能,拓广了top-hat算子的应用范围.     

瞬态非傅里叶导热效应判据的探讨

讨论了通用傅里叶导热定律的数学模型,推导了半无限大物体在第一类边界条件下的基于非傅里叶导热定律的双曲线型偏微分方程的解析解。通过分析非傅里叶导热定律在瞬态条件下温度分布的变化过程,提出了非傅里叶导热效应的瞬态判据以及非傅里叶导热的作用范围,对研究工程中瞬态导热问题(如激光处理,电子束处理等)有重要意义。     

数学与物理的导数

这是一篇关于数学和物理中以导数的推广为中心交流的非正式介绍文章。     

Generic entangling through quantum indistinguishability

We present a general scheme for entangling any degree of freedom of two uncorrelated identical particles from independent sources by a combination of two-particle interferometry and which-way detection. We show that this entanglement generation procedure works for completely random initial states of the variable to be entangled. We also demonstrate a curious complementarity exhibited by our scheme and its applications in estimating the generated entanglement as a function of wave packet overlap at the beamsplitter.     

用不确定度评价测量结果中的有效自由度的作用

论述了有效自由度的计算方法及有效自由度量值在分析测量结果中的应用。     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.