Linear scaling of the interlayer relaxations of the vicinal Cu(p,p,p − 2) surfaces with the number of atom-rows in the terraces

We investigate the multilayer relaxation trends in the vicinal Cu(p,p,p − 2) surfaces employing the all-electron full-potential linearized augmented plane-wave method. Calculations are performed for the (3 3 1), (2 2 1), (5 5 3), (3 3 2), (7 7 5), and (4 4 3) surfaces, which have 3, 4, 5, 6, 7, and 8 atom-rows in the terrace, respectively. The following trends are identified: (i) The interlayer relaxations perpendicular to the surface scale almost linearly with the number of atom-rows in the terraces. (ii) The nearest-neighbor distances do not depend on the surface termination, but only on the local coordination. (iii) For Cu(p,p,p − 2) in which the topmost n surface layers have nearest-neighbor coordination smaller than the bulk Cu (calculated for the unrelaxed surfaces), the topmost (n − 1) interlayer spacings (d₁₂, … , d_n−1,n) contract compared with the unrelaxed spacing, while the nth interlayer spacing (d_n,n+1) expands. The next (n − 2) interlayer spacings (d_n+1,n+2, … , d_{2n−2,2n−1}) contract, while the interlayer spacing indicated by d_2n−1,2n expands. A similar rule was found for the relaxations parallel to the surfaces. These trends provide a better understanding of the atomic structure of vicinal Cu surfaces.     

Exact Solutions of Schrödinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.     

Efficient remote preparation of arbitrary twoand three-qubit states via the χ state

The application of χ state are investigated in remote state preparation(RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable.     

关于正系数多项式导数的点态不等式

本文讨论正系数多项式导数的点态不等式,建立相应的结果。     

保守超混沌在数字图像加密中的应用

基于保守超混沌信号,提出一种数字图像加密算法.该算法利用一个5维保守超混沌系统产生5通道时间序列对原图像分别进行RGB三基色像素级和比特级置乱,再对置乱的RGB三基色作异或操作.在此基础上,利用其中一个通道的时间序列作为密钥分别进行一次正向异或操作的扩散和S盒处理,一次反向异或操作的扩散与S盒处理及置乱,得到加密的图像.最后利用直方图、信息熵、密钥空间等安全性指标对该加密算法进行测试,并与一个五维耗散超混沌系统应用于图像加密的实例进行对比.数值结果表明保守混沌应用到数字图像加密的算法具有更高的安全性和可靠性.     

Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters

We present a formulation of quantum mechanics based on the theory of orthogonal polynomials.The wavefunction is expanded over a complete set of square integrable basis where the expansion coefficients are orthogonal polynomials in the energy and physical parameters. Information about the corresponding physical systems(both structural and dynamical) are derived from the properties of these polynomials. We demonstrate that an advantage of this formulation is that the class of exactly solvable quantum mechanical problems becomes larger than in the conventional formulation(see, for example, table 3 in the text). We limit our investigation in this work to the Askey classification scheme of hypergeometric orthogonal polynomials and focus on the Wilson polynomial and two of its limiting cases(the Meixner–Pollaczek and continuous dual Hahn polynomials). Nonetheless, the formulation is amenable to other classes of orthogonal polynomials.     

量子多体系统的线性张量重正化群方法

文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.