应用约化密度保真度确定自旋为1的一维量子Blume—Capel模型的基态相图

约化密度保真度（reducedensityfidelity）可以用来描述量子多体系统的量子相变,其是两个约化密度矩阵距离的度量．本文应用MERA（multi—scaleentanglementreorganizationansatz）算法,模拟自旋为1的一维量子Blume-Capel模型,并通过对约化密度保真度的计算,确定出其基态相图．单点和两点约化密度矩阵所包含的至关重要的信息的量是不同的,其会体现在约化密度保真度上．另外,本文还从局域序参量和系统能隙的角度,来探讨量子多体系统的相变．     

与光场依赖强度耦合下运动纠缠双原子的周期量子回声

本文将Tavis-Cummings (T-C)模型推广到同时考虑原子运动及与光场依赖强度耦合的情况.运用全量子理论,研究了与光场依赖强度耦合下运动纠缠双原子量子态保真度演化.采用数值计算的方法,探讨了双原子初始纠缠因子θ、光场平均光子数n以及场模结构参量p对双原子量子态保真度演化的影响,解析分析了双原子周期量子回声的形成规律,揭示了其物理实质.结果表明,在场模结构参量p=1的情况下,无论光强和双原子初始纠缠因子如何取值,双原子均产生周期2π的量子回声;在强相干场n=30条件下,改变P从1到小于800时,Bell态双原子产生2π/P周期量子回声.当p≥800时,无论光场是真空场、弱相干场或强相干场,双原子量子态保真度恒为1,即第一类Bell态原子持续处于保真态;而当双原子初始纠缠因子为3π/4时,无论n、p取何值,双原子量子态保真度保持为1,双原子持续处于第二类Bell态的保真态.其结论表明,该推广模型具有很好的双原子周期量子回声性质,为纠缠双原子信息高保真输出及噪音环境下量子信息处理的实验实现提供了理论参量和物理载体.     

带异号电荷两绝缘小球对心正碰的运动学方程

本文利用分离变量求解微分方程和换元积分法推导出带异号电荷的两绝缘小球发生对心正碰的运动学方程,从而得以掌握运动小球在任一时刻的运动状态.     

Invariants for Automorphisms of the Underlying Algebras Relative to Lie Algebras of Cartan Type

Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.     

幂次为3 和4 的整数变量非线性型的整数部分

本文利用Davenport-Heilbronn 方法证明了对于自然数x_j, 表达式
λ₁x₁³+λ₂x₂³+λ₃x₃³+λ₄x₄⁴+λ₅x₅⁴+λ₆x₆⁴
的整数部分在给定条件下可表示无穷多素数, 深化了Brüdern 等人的广义Riemann 假设下等幂次的结果.     

Lie Symmetries, Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System

We study the perturbation to symmetries and adiabatic invariants of a generalized Birkhoff system. Based on the invariance of differential equations under infinitesimal transformations, Lie symmetries, laws of conservations, perturbation to the symmetries and adiabatic invariants of the generalized Birkhoff system are presented. First, the concepts of Lie symmetries and higher order adiabatic invariants of the generalized Birkhoff system are proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate the method and results.     

Efficient Polarization Entanglement Purification Using Spatial Entanglement

The protocol using spatial entanglement to purify polarization entanglement by entanglement transformation between different degrees of freedom in a realistic environment is elaborated. Our analyses show that the bit-flip error can be completely purified, but the pure maximally entangled state can not be obtained ultimately if the spatial entanglement is impure. The fidelity of the purified state is decided by the spatial entanglement. Furthermore, this protocol can also be extended to purify the multi-particle Greenberg—Horne—Zeilinger （GHZ） state. It is presented that the spatial entanglement can be served as another source to improve the quality of entanglement.     

Modulational Instability and Variable Separation Solution for a Generalized （2＋1）-Dimensional Hirota Equation

It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.     

三光子纠缠W态隐形传输令牌总线网的保真度计算

计算了三光子W态隐形传输令牌总线网的保真度.通过计算发现在整个量子网络通信过程中,对于给定的分析角θ,保真度仅与系数|a|2有关;随着分析角θ的增加,保真度出现最大值所对应的系数|a|2相应减小,取θ=π/4、π/2、3π/4时可使保真度达最大值1,此时对应的|a|2分别为0.724、0.5和0.276.对于给定的系数|a|,保真度仅与分析角θ有关;若|a|=0,则无论θ为何值,保真度始终为0;若|a|=|b|=0.7071,则当θ=π/2、3π/2时保真度达最大值1.     

贝尔特拉米微分参数的历史作用

19世纪,数学经历着巨大的变革,微分几何以及代数实现了近代向现代的转化.其中,贝尔特拉米微分参数是这段历史当中作用很大的成果,它对弹性力学、电磁学、势论以及张量分析都有重要作用,尤其以张量分析为主要.