Entanglement Degree in the Time Development of the Jaynes–Cummings Model

Recently, it has been become known that a quantum entangled state plays an important role in fields of quantum information theory, such as quantum teleportation and quantum computation. Research on quantifying entangled states has been carried out using several measures. In this Letter, we will adopt this method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes–Cummings model.     

Energy spectrum of fast atoms in a dark cathode space

A method is proposed for solving the kinetic equation for fast atoms moving in a proper gas. We find the Green's function which permits computation of the energy spectrum of fast atoms for an arbitrary source function in the volume of a proper gas or an amorphous body having plane boundaries. The energy spectrum of fast atoms is computed in a dark cathode space. The solution obtained is used to compute the contribution of fast atoms to atomization of the cathode surface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 62–67, August, 1987.     

Sound propagation over ground: Analytical approximations and experimental results

Approximations of the sound field emitted by a point source in the presence of the ground have recently been developed [1]. In this paper, these analytical expressions, slightly improved for computation, are compared with an exact representation of the sound pressure and two kinds of experimental results. The approximations, easy to compute, provide a reasonable accuracy for predictions of the sound levels in the asymptotic and intermediate (preceding the asymptotic) regions. Furthermore, numerical techniques (an optimization method) are presented for obtaining the “best value” of the ground normal impedance, from data obtained in Kundt's tube and far field measurements.     

Testing the Universality of Free Fall for Charged Particles in Space

At first a short analysis of the notion of the Universality of Free Fall (UFF) for charged matter is given. Even if neutral bound systems of charged particles are in full accordance with the UFF, there is still a possibility that an isolated charge couples anomalously to gravitational fields. The experiment of Witteborn and Fairbank aimed at testing the UFF for electrons is shortly reviewed emphasizing the various additional disturbing gravity induced electromagnetic fields. Since these additional gravity induced fields are not very well under control, a space borne version of this experiment will reduce these disturbances considerably. The corresponding estimates for these kinds of tests in space are presented. As a result, gravity–induced stray field can be reduced considerably. Furthermore, also patch–effects can be reduced efficiently due to novel coating techniques. Therefore, due to microgravity conditions and new techniques the UFF for charged particles may be tested with much higher accuracy than in previous experiments.     

线指数特征空间内恒星光谱离群数据挖掘与分析

大规模光谱巡天将产生海量的光谱数据,为搜寻一些奇异甚至于未知类型的光谱提供了机会,对这些特殊天体的研究有助于揭示宇宙的演变规律和生命起源,巡天数据的离群数据挖掘有助于这些特殊的光谱的发现。利用线指数对光谱数据进行降维能够在尽可能多的保留光谱物理特征的同时,有效解决高维光谱数据聚类分析中运算复杂度较高的问题。提出了基于线指数特征的海量恒星光谱离群数据挖掘及分析的方法,以恒星光谱的Lick线指数作为光谱数据的特征,利用聚类搜寻离群数据的方法在海量光谱巡天数据搜寻离群数据,以此为基础并给出线指数特征空间内离群光谱数据的分析方法。实验结果证明:(1)以线指数作为光谱的特征值能快速的完成对高维光谱数据的离群数据挖掘,可以解决高维光谱数据运算复杂度高的问题;(2)该方法是在聚类结果上进行的离群数据挖掘,能够有效的挖掘出数量较少的发射线恒星、晚M型恒星、极贫金属星、缺失数据光谱等数据;(3)线指数特征空间的离群数据挖掘可以得到线指数特征空间内特殊恒星的发现规则。本文所提出的基于线指数特征的离群数据挖掘及分析方法可以应用到巡天数据的相关研究中。     

Torsion,Scalar Field,Mass and FRW Cosmology

In the Einstein–Cartan space U₄, an axial vector torsion together with a scalar field connected to a local scale factor have been considered. By combining two particular terms from the SO(4, 1) Pontryagin density and then modifying it in a SO(3, 1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then under FRW-cosmological background, where the scalar field is connected to the source of gravitation, the Euler–Lagrange equations ultimately give the constancy of the gravitational constant together with only three kinds of energy densities representing mass, radiation and cosmological constant. The gravitational constant has been found to be linked with the geometrical Nieh-Yan density.     

A continuation BSOR-Lanczos–Galerkin method for positive bound states of a multi-component Bose–Einstein condensate

We develop a continuation block successive over-relaxation (BSOR)-Lanczos–Galerkin method for the computation of positive bound states of time-independent, coupled Gross–Pitaevskii equations (CGPEs) which describe a multi-component Bose–Einstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a single-component BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multi-component BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a two/three-component BEC are solved efficiently and reliably by the continuation BSOR-Lanczos–Galerkin method.     

A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

In this paper, we extend the earlier work [M. Barrault, Y. Maday, N. C. Nguyen, A.T. Patera, An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations, C.R. Acad. Sci. Paris, Série I 339 (2004) 667–672; M.A. Grepl, Y. Maday, N.C. Nguyen, A.T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, M2AN Math. Model. Numer. Anal. 41 (3) (2007) 575–605.] to provide a posteriori error estimation and basis adaptivity for reduced-basis approximation of linear elliptic partial differential equations with nonaffine parameter dependence. The essential components are (i) rapidly convergent reduced-basis approximations – (Galerkin) projection onto a space spanned by N global hierarchical basis functions which are constructed from solutions of the governing partial differential equation at judiciously selected points in parameter space; (ii) stable and inexpensive interpolation procedures – methods which allow us to replace nonaffine parameter functions with a coefficient-function expansion as a sum of M products of parameter-dependent coefficients and parameter-independent functions; (iii) a posteriori error estimation – relaxations of the error-residual equation that provide inexpensive yet sharp error bounds for the error in the outputs of interest; (iv) optimal basis construction – processes which make use of the error bounds as an inexpensive surrogate for the expensive true error to explore the parameter space in the quest for an optimal sampling set; and (v) offline/online computational procedures – methods which decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter value, we calculate the output of interest and associated error bounds – depends only on N, M, and the affine parametric complexity of the problem; the method is thus ideally suited for repeated and reliable evaluation of input–output relationships in the many-query or real-time contexts.     

Proca Effect in Kerr–Newman Metric

The Proca effect of an electric field is studied in curved space. A Kerr–Newman metric with the photon rest mass can be presented by the analytic continuation (Xu, C. M. (....). General Relativity and Modern Cosmology, Nanking Normal University) in a short range. It yields the correction in the Kerr–Newman space.     

Blind quantum computation with identity authentication

Blind quantum computation (BQC) allows a client with relatively few quantum resources or poor quantum technologies to delegate his computational problem to a quantum server such that the client's input, output, and algorithm are kept private. However, all existing BQC protocols focus on correctness verification of quantum computation but neglect authentication of participants' identity which probably leads to man-in-the-middle attacks or denial-of-service attacks. In this work, we use quantum identification to overcome such two kinds of attack for BQC, which will be called QI-BQC. We propose two QI-BQC protocols based on a typical single-server BQC protocol and a double-server BQC protocol. The two protocols can ensure both data integrity and mutual identification between participants with the help of a third trusted party (TTP). In addition, an unjammable public channel between a client and a server which is indispensable in previous BQC protocols is unnecessary, although it is required between TTP and each participant at some instant. Furthermore, the method to achieve identity verification in the presented protocols is general and it can be applied to other similar BQC protocols.