A Scheme for Connecting Quantum Components

We propose an approach to connect components of a quantum computer by using a linear cluster state, with which an arbitrary N-particle state can be perfectly propagated between quantum components in two ways that are based on feedback measurements and local transformation.     

A Scheme for Dense Coding in the Non-Symmetric Quantum Channel

We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver‘s particles sharing the quantum maximally entangled state. The efficiency of gaining classical information is also considered.We conclude that when a more level particle is with the sender, she can obtain a non-symmetric quantum channel from a symmetric one by entanglement transfer. Thus the efficiency of information transmission is improved.     

New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System

For a relativistic Hamiltonian system,two new types of the Lie symmetries and conservation laws are given under infinitesimal transformaitons of groups.On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t,generalized coordinates qs and generalized monenta ps,we obtain the determinging equations,the structure equations and the conserved quantities of the Lie symmetries.Introducing infinitesimal transformation for generalized coordinates qs and generalized momenta ps,we construct the Lie symmetrical transformations of the system,which only depend on the canonical variables.A set of conserved quantities are directly obtained from the Lie symmetries of the syste.An example is given to illustrante the application of the results.     

Integrating Factors and Conservation Theorems for the Nonholonomic Singular Lagrange System

We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.     

Further Study on the Conservation Laws of?Energy-Momentum Tensor Density for a Gravitational System

The various methods to derive Einstein conservation laws and the relevant definitions of energy-momentum tensor density for gravitational fields are studied in greater detail. It is shown that these methods are all equivalent. The study on the identical and different characteristics between Lorentz and Levi-Civita conservation laws and Einstein conservation laws is thoroughly explored. Whether gravitational waves carry the energy-momentum is discussed and some new interpretations for the energy exchanges in the gravitational systems are given.     

Scheme for Robust Long-Distance Continuous Variable Quantum Key Distribution

It is shown that the configuration of phase coding for quantum key distribution with single photon can also be used for continuous variable quantum key distribution. Therefore the robust long-distance high-speed quantum key distribution can be achieved with current technology.     

Symplectic Schemes and the Shooting Method for Eigenvalues of the Schrodinger Equation

The one-dimensional time-independent Schr6dinger equation is transformed into a Hamiltonian canonical equation by means of the Legendre transformation, then the symplectic schemes and a new shooting method extended to the eigenvalues of the Schr6dinger equation. The method is applied to the calculations of one-dimensional harmonic oscillator, an anharmonic oscillator and the hydrogen atom. The numerical results are in good agreement with the exact ones.     

Novel Scheme for Narrow Band Fiber Filter System

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Efficient Scheme for One-Way Quantum Computing in Thermal Cavities

We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box⁽⁴⁾ configuration, we then implement Grover’s search algorithm for four database elements in a very simple way as an example of one-way quantum computing.     

Birkhoffian Symplectic Scheme for a Quantum System

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.     

高阶辛算法在典型量子器件模拟中的应用

利用辛积分和高阶交错差分方法建立了求解含时薛定谔方程的高阶辛算法(SFDTD(4,4)).对空间部分的二阶导数采用四阶准确度的差分格式离散得到随时间演化的多维系统再引入四阶辛积分格式离散;探讨了SFDTD(4,4)法的稳定性,获得了含时薛定谔方程的一维以及多维的稳定性条件,并得到在含势能情况下该稳定性条件的具体表达式;借助复坐标沿伸概念,实现了SFDTD(4,4)法在量子器件模拟中的完全匹配层吸收边界条件.结合一维量子阱和金属场效应管传输的仿真,结果表明较传统的时域有限差分算法,SFDTD(4,4)有着更好的计算准确度,适用于长时间仿真.算法及相关结果可为实际量子器件的设计提供必要的参考.     

二维非定常Sine-Gordon方程辛算法及其孤子数值模拟

在矩形域[-a,a]×[-a,a]内对微分算子L=(ə²)/(əx²)+(ə²)/(əy²)用5点差分格式将二维非定常Sine Gordon方程离散化为一个2×799²阶非线性Hamilton系统.对该系统使用Euler中心格式,得到一个非线性方程组.对此方程组建立迭代解法并给出了这个迭代方法的收敛条件和收敛速度.Sine Gordon方程单孤子和双孤子的数值模拟试验显示该辛算法是有效的.     

强激光场中CO分子经典轨迹的辛算法

采用辛算法计算CO异核双原子分子系统在强激光场作用下的经典轨迹,与Runge-Kutta方法进行比较,分析了CO双原子分子在激光场作用下的振动轨迹、相平面轨道与总能量随时间的变化及CO分子的解离.     

SRLW方程的多辛Fourier谱格式及其守恒律

通过引进正则动量,将对称正则长波方程（简称SRLW方程）转化成多辛形式的方程组,它具有多辛守恒律;介绍了空间方向满足周期边界条件的函数的Fourier谱方法;对SRLW方程的多辛方程组在空间方向利用Fourer谱方法,时间方向上应用Euler中点格式离散,得到其多辛Fourier拟谱格式;证明此格式的一些离散守恒律．用此格式模拟了SRLW方程的单个孤立波,还模拟了多个孤立波的追赶、碰撞和分离过程．     

Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System

In this paper, we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system. We consider the situation in which the unknown function and its first-order derivative are given at the boundary. The scheme is shown to have high order convergence. Numerical examples are given to verify the theoretical results.     

单个守恒型方程熵耗散格式中熵耗散函数的构造

对于一维单个守恒律方程,文[8]设计了一种非线性守恒型差分格式.此格式为二阶Godunov型的,用的是分片线性重构(reconstruction),重构函数的斜率是根据熵耗散得到的.格式满足熵条件.与传统的守恒格式不同的是此格式在计算过程中不仅用到了数值解还用到了数值熵.在此格式中一个所谓的熵耗散函数起到了很重要的作用,它在每一个网格的计算中耗散熵,以保证格式满足熵条件.文[8]中设计的熵耗散函数比较复杂,并且不是很完善.故数值地分析了在格式的构造中为何应给熵以一定的耗散,及应耗散多少.并且给出了一个新的以数值解的二阶差分作为基本模块的熵耗散函数.最后给出了相应的数值算例.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

BS分子α带系A~2Π→X~2Σ~+及γ带系C~2Π→X~2Σ~+法兰克-康登因子的计算

在双原子分子核运动的薛定谔方程中，计入分子的振转相互作用项，在Ｍｏｒｓｅ势近似下得出的波函数除与振动量子数有关外，还与转动量子数有关。本文用该波函数编程计算了ＢＳ分子α带系Ａ２Π→Ｘ２Σ＋及γ带系Ｃ２Π→Ｘ２Σ＋法兰克－康登（Ｆｒａｎｃｋ－Ｃｏｎｄｏｎ）因子（简称Ｆ－Ｃ因子）。计算中转动量子数的取值由Ｊ＝０至Ｊ＝２００，其结果适用于低温、高温和强激波条件。