Generic entangling through quantum indistinguishability

We present a general scheme for entangling any degree of freedom of two uncorrelated identical particles from independent sources by a combination of two-particle interferometry and which-way detection. We show that this entanglement generation procedure works for completely random initial states of the variable to be entangled. We also demonstrate a curious complementarity exhibited by our scheme and its applications in estimating the generated entanglement as a function of wave packet overlap at the beamsplitter.     

On many‐sorted algebraic closure operators

A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many‐sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Fock Theories and Quantum Logics

The notion of Fock theory is introduced in the framework of quantum logics, which are here orthomodular atomic lattices satisfying the covering property. It is shown that there are some fundamental facts concerning particles, which may be successfully discussed in this general context. One of these facts is to establish the theoretical conditions for considering particles as sharply defined entities. The other refers to the theoretical circumstances, which almost impose to consider that some particles have a structure, meaning they are composed from other particles. This last problem is strongly related with the conservative time evolutions.     

Accurate double many‐body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single‐sheeted double many‐body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the and dissociation channels involving nitrogen in the ground and first excited states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner–Teller degeneracy of the and states of . Such a work can both be recommended for dynamics studies of the reaction and as building blocks for constructing the double many‐body expansion potential energy surface of larger nitrogen/hydrogen‐containing systems. In turn, a test theoretical study of the reaction has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result. © 2013 Wiley Periodicals, Inc.     

纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

多节摆的自由振动分析

利用拉格朗日方程,导出了多节摆系统的运动微分方程.根据三对角阵的性质,给出了振动系统的特征多项式和特征矢量的递推公式,并以三节摆为例,说明了结果的应用,用此方法验证了<力学与实践>2002年第24期<多自由度振动系统的简正坐标和简正振动模式>一文中的结果.     

Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian

For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points (according to Motreanu and Panagiotopoulos (“Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities,” Nonconvex Optimization Applications, Vol. 29, Kluwer, Dordrecht, 1998, Chap. 3)) is established by mainly adapting a new technique due to Ricceri (2000, J. Comput. Appl. Math.113, 401-410). Two applications are then presented. Both of them treat the Neumann problem for an elliptic variational-hemivariational inequality with p-Laplacian.     

An asymptotic minimax risk bound for estimation of a linear functional relationship

We consider estimation of the parameter B in a multivariate linear functional relationship X_i=ξ_i+ξ_1i, Y_i=Bξ_i+ξ_2i, i=1,…,n, where the errors (ζ_1i^′, ζ_2i^′) are independent standard normal and (ξ_i, i ) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n^−1/2 is also established.     

Comparison of CEPA and CP-MET methods

The known CEPA variants CEPA (v) withv = 0,1,2,3 and two new ones withv = 4, 5 are compared both formally and for various numerical examples with CP-MET. The main conclusions are: 1. In those situations where both CP-MET and the CEPA variants are justified (i.e. for “good” closed shell states) the correlation energies obtained with the 7 different schemes differ very little (by something like ±2%), with CEPA (1) closest to CP-MET (difference usually a fraction of 1%) and CEPA (4) nearly as close; this is rather insensitive to whether one uses canonical or localized orbitals. Even CEPA (3) is not too far from CP-MET, which confirms an earlier suggestion of Kelly. 2. In those cases where one of the 7 schemes fails (e.g. due to near degeneracy as in covalent molecules at large internuclear distances) the other 6 usually fail as well, though CEPA (0) is then somewhat poorer than the other schemes. Then no longer CEPA (1) but rather CEPA (3) is closest to CP-MET and then all schemes converge much better in a localized representation. 3. CEPA (2) usually leads to best agreement with experiment since it simulates to some extent triple substitutions. In none of the studied examples does CP-MET show a significant superiority as compared to the other schemes. Possible improvements to extend the domain of applicability of these methods are discussed.