2017年, 第68卷, 第04期　
刊出日期：2017-10-01

  

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  Quantifying Spontaneously Symmetry Breaking of Quantum Many-Body Systems

  董国慧, 房一楠, 孙昌璞

  理论物理通讯. 2017, 68(04): 405-411.

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  Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry-breaking phase. We study the spontaneous symmetry breaking in the conventional superconductor and Bose-Einstein condensation with a continuous measure of symmetry by showing that both the many-body systems can be mapped into the many spin model. We also formulate the underlying relation between the spontaneous symmetry breaking and the order parameter quantitatively. The degree of symmetry stays unity in the absence of the two emergent phenomena, while decreases exponentially at the appearance of the order parameter which indicates the inextricable relation between the spontaneous symmetry and the order parameter.
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  Reflection and Transmission Coefficients of the Symmetric Barrier-Type Shifted Deng-Fan Potential

  Oluwatimilehin Joshua Oluwadare, Kayode John Oyewumi, Karl-Eric Thylwe, Somayyeh Hassanabadi

  理论物理通讯. 2017, 68(04): 412-416.

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  By applying continuity and boundary conditions, the reflection and transmission coefficients of onedimensional time-independent Schrödinger equation with a symmetric barrier-type shifted Deng-Fan potential are obtained and discussed. The numerical and graphical results are very sufficient, accurate and consistent with the conservation of probability.
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  Exact Solutions, Symmetry Reductions, Painlevé Test and Bäcklund Transformations of A Coupled KdV Equation

  徐敏慧, 贾曼

  理论物理通讯. 2017, 68(04): 417-424.

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  A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ⁴ model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Painlevé test shows the coupled KdV equation possesses Painlevé property. The Bäcklund transformations of the coupled KdV equation related to Painlevé property and residual symmetry are shown.
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  Initial-Boundary Value Problem for Two-Component Gerdjikov-Ivanov Equation with 3×3 Lax Pair on Half-Line

  朱巧珍, 范恩贵, 徐建

  理论物理通讯. 2017, 68(04): 425-438.

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  The Fokas unified method is used to analyze the initial-boundary value problem of two-component Gerdjikov-Ivanonv equation on the half-line. It is shown that the solution of the initial-boundary problem can be expressed in terms of the solution of a 3×3 Riemann-Hilbert problem. The Dirichlet to Neumann map is obtained through the global relation.
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  Majorana Representation and Mean Field Approach for Interacting-Boson System

  刘昊迪, 方杰, 郑泰玉

  理论物理通讯. 2017, 68(04): 439-446.

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  The Majorana representation, which represents a quantum state by stars on the Bloch sphere, provides us an intuitive tool to study the quantum evolution in high dimensional Hilbert space. In this work, we investigate the second quantized model and the mean-field model for the interacting-boson system in the Majorana representation. It is shown that the motions of states in the two models are same in the linear case. Furthermore, the contribution of the nonlinear interaction to the star motions in the second quantized model can be expressed by a single star part which is equal to the nonlinear part of the equation for the star in mean-field model under large boson number limit and an extra part caused by the correlation between stars. These differences and relations can not only be reflected by the population differences between the two boson modes in the two models, but also lie with the differences between the continuous changes of the second quantized evolution with the nonlinear interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect. The reason of the difference between the two models is also discussed by an effective Hamiltonian.
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  Tensor Fields on Self-Dual Warped AdS₃ Background

  Mohammad A. Ganjali, Sadegh Sadeghian

  理论物理通讯. 2017, 68(04): 447-454.

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  Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3-dimensional self-dual space-like warped AdS₃ black hole background. We obtain a Klein-Gordon-like equation for tensor fields. By using gauge constraint and traceless condition, we will find the exact solutions of the equations of motion. Then, we will compute the quasi-normal modes by imposing appropriate boundary conditions at horizon and infinity.
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  Uniqueness of First Order Post-Newtonian Collinear Solutions for Three-Body Problem under a Scalar-Tensor Theory

  曹伟光, 周天倚, 谢懿

  理论物理通讯. 2017, 68(04): 455-462.

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  As a continuing investigation of an earlier work that establishes the collinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System.
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  A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r-Matrix Method

  张玉峰, Iqbal Muhammad, 岳超

  理论物理通讯. 2017, 68(04): 463-470.

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  We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov-Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well.
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  Influences of Fractal Substrate Structures on Dynamic Scaling Behaviors of Etching Model

  宋丽建, 唐刚, 寻之朋, 郝大鹏, 陈祎力, 张哲

  理论物理通讯. 2017, 68(04): 471-477.

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  The Etching model on various fractal substrates embedded in two dimensions was investigated by means of kinetic Mento Carlo method in order to determine the relationship between dynamic scaling exponents and fractal parameters. The fractal dimensions are from 1.465 to 1.893, and the random walk exponents are from 2.101 to 2.578. It is found that the dynamic behaviors on fractal lattices are more complex than those on integer dimensions. The roughness exponent increases with the increasing of the random walk exponent on the fractal substrates but shows a non-monotonic relation with respect to the fractal dimension. No monotonic change is observed in the growth exponent.
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  Vortex and Gaussian Solitons of (3+1)-Dimensional Spatially Modulated Cubic-Quintic-Septimal Nonlinear Schrödinger Equation with External Potential

  徐云杰

  理论物理通讯. 2017, 68(04): 478-482.

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  Based on the variable separation principle and the similarity transformation, vortex soliton solution of a (3+1)-dimensional cubic-quintic-septimal nonlinear Schrödinger equation with spatially modulated nonlinearity under the external potential are obtained in the spatially modulated cubic-quintic-septimal nonlinear media. If the topological charge m=0 and m≠0, Gaussian solitons and vortex solitons can be constructed respectively. The shapes of vortex soliton possess similar structures when the value of l-m is same. Moreover, all phases of vortex solitons exist m-jump with the change of every jump as 2π/m, m-jumps, and thus totally realize the azimuthal change of 2π around their cores.
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  Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

  宋晓娜, 宋帅, Inés Tejado Balsera, 刘磊坡

  理论物理通讯. 2017, 68(04): 483-494.

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  This paper investigates the mixed H_∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H_∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H_∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.
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  Polar-Core Spin Vortex of Quasi-2D Spin-2 Condensate in a Flat-Bottomed Optical Trap

  郑公平, 常高瞻, 李频, 李婷

  理论物理通讯. 2017, 68(04): 495-499.

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  Motivated by the recent experiments realized in a flat-bottomed optical trap[Science 347 (2015) 167; Nat. Commun. 6 (2015) 6162], we study the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a homogeneous trap plus a weak magnetic field. The exact spatial distribution of local spin is obtained and the vortex core are observed to decrease with the growth of the effective spin-spin interaction. For the larger effective spin-spin interaction, the spatial distribution of spin magnitude in spin-2 condensate we obtained agrees well with that of spin-1 condensate in a homogeneous trap, where a polar-core spin vortex was schematically demonstrated as a fully-magnetized planar spin texture with a zero-spin core. The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap, simultaneously. Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.
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  Centrality Dependence of K^*(892)⁰ and φ(1020) Production at LHC

  Inam-ul Bashir, Saeed Uddin

  理论物理通讯. 2017, 68(04): 500-504.

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  We study the centrality dependence of the mid-rapidity (|y|< 0.5) yields and transverse momentum distributions of K^*(892)⁰ and φ(1020) resonances produced in Pb + Pb collisions at √s_NN=2.76 TeV. The midrapidity density (dN/dy) and the shape of the transverse momentum spectra are well reproduced by an earlier proposed Unified Statistical Thermal Freeze-out Model (USTFM), which incorporates the effects of both longitudinal as well as transverse hydrodynamic flow. The freeze-out properties in terms of kinetic freeze-out temperature and transverse flow velocity parameter are extracted from the model fits to the transverse momentum data provided by the ALICE experiment at the LHC. The kinetic freeze-out temperature is found to increase with decreasing event centrality while the transverse flow velocity parameter shows a mild decrease on moving towards peripheral collisions. Moreover the centrality dependence of the mid-rapidity system size at freeze-out has also been studied in terms of transverse radius parameter.
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  Study of Cold Fusion Reactions Using Collective Clusterization Approach

  Gurjit Kaur, Kirandeep Sandhu, Manoj K. Sharma

  理论物理通讯. 2017, 68(04): 505-517.

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  Within the framework of the dynamical cluster decay model (DCM), the 1n evaporation cross-sections (σ_1n) of cold fusion reactions (Pb and Bi targets) are calculated for Z_CN=104-113 superheavy nuclei. The calculations are carried out in the fixed range of excitation energy E_CN^*=15 ±1 MeV, so that the comparative analysis of reaction dynamics can be worked out. First of all, the fission barriers (B_f) and neutron separation energies (S_1n) are estimated to account the decreasing cross-sections of cold fusion reactions. In addition to this, the importance of hot optimum orientations of β_2i-deformed nuclei over cold one is explored at fixed angular momentum and neck-length parameters. The hot optimum orientations support all the target-projectile (t,p) combinations, which are explored experimentally in the cold fusion reactions. Some new target-projectile combinations are also predicted for future exploration. Further, the 1n cross-sections are addressed for Z_CN=104-113 superheavy nuclei at comparable excitation energies which show the decent agrement with experimental data upto Z_CN=109 nuclei. Finally, to understand the dynamics of higher-Z superheavy nuclei, the cross-sections are also calculated at maximum available energies around the Coulomb barrier and the effect of non-sticking moment of inertia (I_NS) is also investigated at these energies.
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  MHD Flow and Heat Transfer of a Generalized Burgers' Fluid due to a Periodic Oscillating and Periodic Heating Plate

  白羽, 姜月华, 张艳, 赵豪杰

  理论物理通讯. 2017, 68(04): 518-524.

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  This paper investigates the MHD flow and heat transfer of the incompressible generalized Burgers' fluid due to a periodic oscillating plate with the effects of the second order slip and periodic heating plate. The momentum equation is formulated with multi-term fractional derivatives, and by means of viscous dissipation, the fractional derivative is considered in the energy equation. A finite difference scheme is established based on the G1-algorithm, whose convergence is confirmed by the comparison with the analytical solution in an example. Meanwhile the numerical solutions of velocity, temperature and shear stress are obtained. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Increasing the fractional derivative parameter α, the velocity and temperature have a decreasing trend, while the influences of fractional derivative parameter β on the velocity and temperature behave conversely. Increasing the absolute value of the first order slip parameter and the second order slip parameter both cause a decrease of velocity. Furthermore, with the decreasing of the magnetic parameter, the shear stress decreases.
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  Lattice Boltzmann Study on Seawall-Break Flows under the Influence of Breach and Buildings

  梅秋莹, 张文欢, 汪一航, 陈文文

  理论物理通讯. 2017, 68(04): 525-535.

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  In the process of storm surge, the seawater often overflows and even destroys the seawall. The buildings near the shore are usually inundated by the seawater through the breach. However, at present, there is little study focusing on the effects of buildings and breach on the seawall-break flows. In this paper, the lattice Boltzmann (LB) model with nine velocities in two dimensions (D2Q9) for the shallow water equations is adopted to simulate the seawall-break flows. The flow patterns and water depth distributions for the seawall-break flows under various densities, layouts and shapes of buildings and different breach discharges, sizes and locations are investigated. It is found that when buildings with a high enough density are perpendicular to the main flow direction, an obvious backwater phenomenon appears near buildings while this phenomenon does not occur when buildings with the same density are parallel to the main flow direction. Moreover, it is observed that the occurrence of backwater phenomenon is independent of the building shape. As to the effects of breach on the seawall-break flows, it is found that only when the breach discharge is large enough or the breach size is small enough, the effects of asymmetric distribution of buildings on the seawall-break flows become important. The breach location only changes the flow pattern in the upstream area of the first building that seawater meets, but has little impact on the global water depth distribution.
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  DFT Investigation of Structural, Electronic, Elastic and Optical Properties of SrMO₄ (M=Mo and W)

  Hamza Gueffaf, Brahim Lagoun, Abdelnasser Guibadj, Said Maabed, Ahmed Gueddouh

  理论物理通讯. 2017, 68(04): 536-544.

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  A planes waves pseudo-potential calculations are performed for the SrMO₄ (M=Mo and W) compound in order to investigate the structural, electronic, elastic and optical properties. The calculated lattice constants are in good agreement with experiment ones. The electronic structures show that SrMO₄ has a direct band gap situated at Γ point. The calculated elastic constants indicate that both structures are mechanically stable. The bulk modulus, shear modulus, Young's modulus and Poisson ratio are investigated from the elastic constants, in the same time the anisotropy of the elastic properties is discussed. The imaginary part of the dielectric functions is calculated and the contributions of various transitions peaks are analyzed. Furthermore, the other optical properties such as absorption coefficient I(ω), optical reflectivity R(ω), energy-loss spectrum L(ω), and the refractive index n(ω) have been investigated.
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  SEIR Model of Rumor Spreading in Online Social Network with Varying Total Population Size

  董苏雅拉图, 邓燕斌, 黄永畅

  理论物理通讯. 2017, 68(04): 545-552.

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  Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.
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  Effects of Anisotropy on Scalar Field Ghost Dark Energy and the Non-Equilibrium Thermodynamics in Fractal Cosmology

  A. Najafi, H. Hossienkhani

  理论物理通讯. 2017, 68(04): 553-564.

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  Since the fractal cosmology has been created in early universe, therefore their models were mostly isotropic. The majority of previous studies had been based on FRW universe, while in the early universe, the best model for describing fractal cosmology is actually the anisotropic universe. Therefore in this work, by assuming the anisotropic universe, the cosmological implications of ghost and generalized ghost dark energy models with dark matter in fractal cosmology has been discussed. Moreover, the different kinds of dark energy models such as quintessence and tachyon field, with the generalized ghost dark energy in fractal universe has been investigated. In addition, we have reconstructed the Hubble parameter, H, the energy density, ρ, the deceleration parameter, q, the equations of state parameter, ω_D, for both ghost and generalized ghost dark energy models. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field according to the evolution of generalized ghost dark energy density. Eventually, thermodynamics of the cosmological apparent horizon in fractal cosmology was investigated and the validity of the Generalized second law of thermodynamics (GSLT) have been examined in an anisotropic universe. The results show the influence of the anisotropy on the GSLT of thermodynamics in a fractal cosmology.