Einstein——Podolsky——Rosen entanglement in time-dependent periodic pumping non-degenerate optical parametric amplifier

The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein-Podolsky-Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.     

Near-infrared fundus camera based on polarization switch in stray light elimination

This letter shows that the human eye fundus tissue has higher reflectivity at the near-infrared (NIR) wavelength, and that some aberrations exist at the pre-optical system from cornea to vitreous. We design a NIR fundus camera with inner focusing, which can be applied to the -10D to 10D range of vision and has the advantage of ensuring the stability of image when is focused. Considered as Liou’s eye aberration model, we correct the integrated aberration to ensure a 100lp/mm resolution when we complete the assembly and calibration of the fundus camera. Kohler illumination is also applied to obtain uniform fundus illumination. Moreover, we put forward a novel method for stray light elimination based on polarization switch, which inhibits ghost image formation near the focal plane when the illumination beam is reflected by the eyepiece surface. The result shows that this method is effective in ensuring an illumination uniformity of 80%, with the advantage of simple structure and easy assembly.     

用推广的等效两体方法求解类氦离子三体问题

介绍了求解三体问题的等效两体方法,将等效两体方法推广到原子系统,利用该方法求解类氦离子的基态,与一般的单参数变分法相比得到了与实验值符合得更好的结果,进而利用双参数变分法对所得结果进行了检验。 结果表明,等效两体方法同样适用于求解原子系统中的三体问题。 An extended equivalent two body method for three body systems is introduced in this article. The method is applied to an atomic three body system. Energies and wave functions of a helium like ion are calculated,which are consistent with the experimental data much better,in contrast to the results obtained by a one parameter calculus of variations approach. Then we use a two parameter calculus of variations approach to verify the precision of the ground state energy and wave function obtained by the extended equivalent two body method. These results indicated that the extended equivalent two body method is applicable to an atomic three body problem.     

The classification and analysis of dynamic networks

In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M--G--P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M--G--P network is not only scale-free but also of a small-world feature in proper conditions.     

Self-attenuation corrections calculated by LabSOCS Simulations for gamma-spectrometric measurements with HPGe detectors

Simulations from Laboratory Sourceless Object Counting System (LabSOCS) software were used to determine self-attenuation correction factor, which is defined as the efficiency ratio of the sample with the absorbing medium to that of the sample without absorbing medium. The semi-empirical self-attenuation correction formula F(μ) used to correct self-attenuation of a sample was applied. A comparison of the two methods reveals that formula of sample with φ 75 mm× 25 mm and φ75 mm× 10 mm can be, respectively, used in the self-attenuation correction for μ in the ranges of 0 to 0.5 cm^-1 and 0.5 cm^-1 to 2.0 cm^-1, indicating that the semi-empirical formula will not be used when μ has exceeded the interval. The semi-empirical formula value is consistent with the experimental value, within 7.9% accuracy. Therefore, this method is correct and effective. Both of our two methods can accurately produce a relative self-attenuation correction factor when the composition of the sample is known. The self-attenuation correction of a sample with unknown composition can only be carried out using a semi-empirical formula method.     

Equivalent Method of Solving Quantum Efficiency of Reflection-Mode Exponential Doping GaAs Photocathode

The mathematical expression of the electron diffusion and drift length LDE of exponential doping photocathode is deduced. In the quantum efficiency equation of the reflection-mode uniform doping cathode, substituting LDE for LD, the equivalent quantum efficiency equation of the reflection-mode exponential doping cathode is obtained. By using the equivalent equation, theoretical simulation and experimental analysis shows that the equivalent index formula and formula-doped cathode quantum efficiency results in line. The equivalent equation avoids complicated calculation, thereby simplifies the process of solving the quantum efficiency of exponential doping photocathode.     

Quasi-Periodic Structures Based on Symmetrical Lucas Function of （2＋1）-Dimensional Modified Dispersive Water-Wave System

By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.     

Addition Formulae of Discrete KP,q-KP and Two-Component BKP Systems

In this paper,we construct the addition formulae for several integrable hierarchies,including the discrete KP,the q-deformed KP,the two-component BKP and the D type Drinfeld–Sokolov hierarchies.With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies,we prove that these addition formulae are equivalent to these hierarchies.These studies show that the addition formula in the research of the integrable systems has good universality.     

New complex variable meshless method for advection-diffusion problems

In this paper,an improved complex variable meshless method(ICVMM) for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square(ICVMLS) approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.     

Quasi Scale-Free Parameter Networks of Ion Source Experiments

We study some parameter networks of ion source adjustment experiments and find quasi-scale-free characters.Their nodes are parameter settings of every discharge and connected by each of adjacent discharge. Their cumulative degree distributions obey the expression of stretched exponential distribution‘s rank-ordering form,and their degree distributions exhibit product-form by two functions, one is similar to an exponential form, and the other is close to a power law. An index is presented to measure how this distribution is close to the power law and how this distribution is used in the analysis of these parameter networks. The mode of parameter adjustment decides that the quasi-scale-free networks are formed naturally.     

Non-contemporaneous variations and Hölder’s principle

In the process of deducing the Hölder principle, a key step is to use the concept of non-contemporaneous variations. In this paper, whether starting from analytic method or from graphic solution method, the authors prove that the expression formula of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree, and obtain a new expression. From the view of calculus of variations and differential calculus, the non-contemporaneous variations are studied. The study result shows that the concept of non-contemporaneous variations is a combination of the concept of variations and the concept of differentiation. The authors prove that the new expression is correct and obtain an equivalent expression of it. By means of this equivalent expression, this paper proves that the above expression formula of non-contemporaneous variations is correct when the variable functions have one-order nearness degree. Further study shows that, in the process of deducing Hölder’s principle, there is an implicit expression. Whether starting from analytic method or from graphic solution method, the authors discovered that the implicit expression of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree and have one-order nearness degree. This paper proves that the implicit expression of non-contemporaneous variations is correct when the variable functions have two-order nearness degree. Further study shows that Hölder’s principle is tenable when the variable functions have two-order nearness degree.     

基于一阶及二阶灰度梯度的散斑图质量评价方法

散斑图质量对数字图像相关(DIC)方法的测量精度具有重要的影响。以平均灰度梯度这一传统的散斑图质量评价参数作为基础,提出了一种新的评价参数——平均一阶及二阶灰度梯度商,该参数同时考虑了一阶和二阶灰度梯度。从整体上来说,一阶灰度梯度的曲面比较光滑,而一阶及二阶灰度梯度商的曲面比较粗糙。采用Zhou等人提出的方法制作了80张模拟散斑图,对这些模拟散斑图的传统参数和提出参数进行了计算。结果表明:当散斑半径相同时,随着散斑数量的增加,两种参数均先增加,后减小;当散斑数量一定时,二者均有一个峰值;散斑半径越大,提出参数的峰值越大,而传统参数的峰值越小。对提出参数的峰值所对应的4张散斑图进行了多次连续平动,并使用DIC方法测量了测点的水平位移。结果表明,在提出参数越大的散斑图上测点的水平位移误差越小,在一定程度上验证了提出参数的正确性。     

具有大范围运动和非线性变形的空间柔性梁在非惯性坐标系下的动力学分析

本文针对具有大范围运动和非线性变形的空间柔性梁, 导出其在运动规律已知的非惯性坐标系下的动力学方程. 通过计算分析, 发现在本文精确模型下, 其各矩阵项较原来的一次耦合模型增加了两类耦合项. 通过仿真研究, 发现由于这两类耦合项的作用造成了附加刚度项K₁、动力刚度项K_d 的变化, 而刚度项对结构的动力学特性具有较大的影响.     

二维非谐振子的束缚态解

讨论势函数为V(ρ)=2ρ λρα的非谐振子的Schr dinger方程。当α=2时其有Hamiltonian量的精确束缚态解。当α3时其有Hamiltonian量的微扰解,尤其是它的一阶、两阶的能量修正及零级、一级波函数。     

弱谐波情况下透射光栅衍射效率标定方法

同步辐射光源中的高次谐波会使透射光栅衍射效率标定精度变差。为了校正光源中的高次谐波对透射光栅衍射效率标定的影响,提出了一种光源存在弱谐波情况下的透射光栅衍射效率标定方法,通过使用谐波X射线的衍射效率修正基波衍射效率标定中谐波的影响,从而得到更为准确的透射光栅衍射效率。使用该标定方法在北京同步辐射光源上开展了透射光栅相对衍射效率标定工作。实验结果表明:在100~800eV存在高次谐波能段,修正后透射光栅一级与零级的相对衍射效率与理论模拟结果吻合较好,修正后光栅二级与一级的相对衍射效率更接近理论模拟结果,但与理论模拟结果仍有较大偏差,该偏差主要来源光栅较弱的二级衍射。     

Soliton,breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints

The nonlinear Schro¨dinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schro¨dinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schro¨dinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.     

平面柔性梁的刚-柔耦合动力学特性分析与仿真

针对大范围运动规律为未知的刚-柔耦合系统研究其动力学特性.利用有限元方法对柔性梁进行离散,采用Lagrange方程建立平面柔性梁的刚-柔耦合动力学方程,研究在大范围运动为自由情况下,平面柔性梁的大范围运动和变形运动的相互耦合机理,比较零次模型、一次耦合模型及精确模型的差异,探讨各种模型的适用性. 关键词： 平面柔性梁 刚-柔耦合系统 动力学特性 分析与仿真     

A new differential calculus on a complex banach space with application to variational problems of quantum theory

It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banach spaces. It is shown that this result makes the calculus largely inapplicable to the solution of variational problems of quantum mechanics. A new concept of differentiability called semi-differentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-valued functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (1969) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus on banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear functions as particular cases.     

Single photon and nonlocality

In a paper by Home and Agarwal [1], it is claimed that quantum nonlocality can be revealed in a simple interferometry experiment using only single particles. A critical analysis of the concept of hidden variable used by the authors of [1] shows that the reasoning is not correct.      

A NUMERICAL COMPARISON OF ALTERNATIVE GALERKIN METHODS FOR EIGENVALUE ESTIMATION

This paper provides a concise and unified comparison of four distinct variations of Galerkin's method. The four Galerkin variations are the explicit (traditional), implicit, quadratic implicit, and diagonalized-implicit Galerkin methods. Results indicate that the explicit Galerkin method is superior to all implicit formulations. Among the implicit methods, the quadratic implicit and diagonalized-implicit perform equivalently and are significantly better than the standard implicit method. The explicit method is recommended in all the cases except those in which the number of trial functions is so large that numerical conditioning affects the eigenvalue estimate. In this case, the diagonalized-implicit method is recommended.