Barriola-Vilenkin黑洞的统计熵

利用量子统计方法 ,直接计算Barriola_Vilenkin黑洞背景下玻色场和费米场的配分函数 ,然后利用砖墙膜模型计算和讨论黑洞背景下玻色场和费米场的熵     

二次谐波系统在浑沌态下的光子统计

数值分析了调制泵浦作用下的二次谐波产生系统的浑沌动力学行为.考虑到混沌运动的遍历性,提出一种研究浑沌态光场光子统计的数值方法,即通过数值积分求解系统动力学方程估计光子数的系统平均.运用这一方法于二次谐波系统,计算了其在浑沌态下的光子统计分布,结果表明是一种超Poisson分布.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

加速牛顿迭代收敛的新方法

提出了加速牛顿迭代收敛的新思想，构造出一类加权牛顿迭代格式，通过选取最优加权因子，使得该格式具有高阶收敛性和较小的渐近误差常数。     

对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Implementation of some higher-order convection schemes on non-uniform grids

A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second-order upwind (SOU) scheme and the second-order hybrid scheme (SHYBRID) on non-uniform grids. The implementation method is simple. The accuracy and efficiency of these higher-order schemes on non-uniform grids are assessed. Three well-known bench mark convection-diffusion problems and a fluid flow problem are revisited using non-uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two-dimensional non-linear Burgers equations; and (4) a two-dimensional incompressible Navier-Stokes flow which is similar to the classical lid-driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non-uniform grids. Higher accuracy is obtained for fewer grid points on non-uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non-uniform grid points is properly chosen.     

弱混强平稳序列随机容量、随即秩次序统计量的极限分布律

设W(1n)W2(n)…W(nn)是严平稳随即序列{Xn,n 1}的前几个变量的顺序统计量,Nn Mn是两正整值r.v,n 1.在较弱一些的混合条件下,本文给出了W(NMn)n标准化后的极限分布,从而使一些提法更趋一般化,主要结果推进了Rao(1984)和张国胜(1993)的工作.由于混合条件的减弱,使得对m-相关和正态平稳过程的具体应用讨论更加充分.     

组合Bose场的分数自旋和分数统计性

对组合Bose子场，采用FS (Faddeev-Senjanovic) 路径积分量子化方法进行量子化.从量子Noether定理出发，给出量子分数自旋和分数统计性质. 关键词： 路径积分量子化 分数自旋 分数统计