2016年, 第66卷, 第04期　
刊出日期：2016-10-01

  

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  On Integrals Involving Universal Associated Legendre Polynomials and Powers of the Factor (1-x²) and Their Byproducts

  孙东升, 尤源, 陆法林, 陈昌远, 董世海

  理论物理通讯. 2016, 66(04): 369-373.

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  The associated Legendre polynomials play an important role in the central fields, but in the case of the non-central field we have to introduce the universal associated Legendre polynomials P_l'^m'(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential. We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor (1-x²)^-p-1 as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction. The calculations are obtained systematically using some properties of the generalized hypergeometric series.
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  Darboux Transformation for a Four-Component KdV Equation

  李年华, 吴丽华

  理论物理通讯. 2016, 66(04): 374-378.

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  With the aid of a gauge transformation, we propose a Darboux transformation for a four-component KdV equation. As an application, we obtain some explicit solutions for the four-component KdV equation.
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  Some (Anti-) Self Duality Solutions on Six Manifolds

  İbrahim Şener

  理论物理通讯. 2016, 66(04): 379-384.

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  The bundle of the 2-forms on 6-manifold decomposes into three subbundles such that Λ²(R⁶)=Λ₁²⊕Λ₆²⊕Λ₈² with dimensions 1, 6 and 8, respectively. The self and anti self duality solutions of the 2-forms, called Φ-duality, are handled and these solutions show that the anti self dual gauge fields live on the subbundles Λ₁² and Λ₆² while the self ones equations on Λ₈². Also the solution on Λ₁² presents a flat connection. In addition, the curvatures of the connections on Λ₆² and Λ₈² have Tr[F³]=0, and so the topological invariants determined by the Chern classes, i.e. topological charge, consist only on the second Chern class. In the result of this case, the anti self and self Φ-dual gauge invariant Lagrangians of defined on both subbundles are bounded by the same topological charge. Also, one gives a quantization case to be relating to the instanton number.
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  A New Integrable (2+1)-Dimensional Generalized Breaking Soliton Equation: N-Soliton Solutions and Traveling Wave Solutions

  Abdul-Majid Wazwaz

  理论物理通讯. 2016, 66(04): 385-388.

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  In this work, we study a new (2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of parameters. We derive multiple soliton solutions, traveling wave solutions, and periodic solutions as well. We use the simplified Hirotas method and a variety of ansatze to achieve our goal.
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  Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

  K. E. Thylwe, O. J. Oluwadare, K. J. Oyewumi

  理论物理通讯. 2016, 66(04): 389-395.

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  A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ε-V₀|<2μ c², where μ is the reduced mass, ε the scattering energy, and V₀ the barrier top energy. The approximate wave numbers are less accurate.
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  Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition

  龚志瑞, 宋智, 孙昌璞

  理论物理通讯. 2016, 66(04): 396-400.

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  We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z₂ topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.
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  General Quantum Meet-in-the-Middle Search Algorithm Based on Target Solution of Fixed Weight

  付向群, 鲍皖苏, 汪翔, 史建红

  理论物理通讯. 2016, 66(04): 401-406.

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  Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is ∑_j^d=(0(√C_n-k+1^d-j)+O(C_k^jlogC_k^j)) with ∑_i=0^dC_kⁱ memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm.
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  Monogamy Relations for Squared Entanglement Negativity

  刘锋

  理论物理通讯. 2016, 66(04): 407-410.

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  This paper contains two main contents. In the first part, we provide two counterexamples of monogamy inequalities for the squared entanglement negativity: one three-qutrit pure state which violates of the He-Vidal monogamy conjecture, and one four-qubit pure state which disproves the squared-negativity-based Regula-Martino-Lee-Adesso-class strong monogamy conjecture. In the second part, we investigate the sharing of the entanglement negativity in a composite cavity-reservoir system using the corresponding multipartite entanglement scores, and then we find that there is no simple dominating relation between multipartite entanglement scores and the entanglement negativity in composite cavity-reservoir systems. As a by-product, we further validate that the entanglement of two cavity photons is a decreasing function of the evolution time, and the entanglement will suddenly disappear interacting with independent reservoirs.
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  Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models

  Shamaila Rani, Abdul Jawad, M. Bilal Amin

  理论物理通讯. 2016, 66(04): 411-422.

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  In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.
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  On d-Dimensional Lattice (co)sine n-Algebra

  姚少魁, 丁璐, 刘鹏, 张春红, 赵伟忠

  理论物理通讯. 2016, 66(04): 423-430.

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  We present the (co)sine n-algebra which is indexed by the d-dimensional integer lattice. Due to the associative operators, this generalized (co)sine n-algebra is the higher order Lie algebra for the n even case. The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values. We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra, respectively. The limiting case of the d-dimensional lattice (co)sine n-algebra is also discussed. Moreover we construct the super sine n-algebra, which is the super higher order Lie algebra for the n even case.
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  Influence of Defects and Crystallographic Orientation on Mechanical Behavior of Nanocrystalline Aluminium

  蔡军, 邓琼, 安敏荣, 宋海洋, 宿梦嘉

  理论物理通讯. 2016, 66(04): 431-438.

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  Simulation of molecular dynamics using Embedded Atom Method (EAM) potentials is performed to investigate the mechanical properties of single crystal Al along various crystallographic orientations under tensile loading. The specimens are provided with one or two embedded circular voids to analyze the damage evolution by void growth and coalescence. The simulation result shows that the Young's modulus, yielding stress and ultimate stress decrease with the emergence of the voids. Besides, the simulations show that the single-crystal Al in different crystallographic orientations behaves differently in elongation deformations. The single-crystal Al with <100> crystallographic orientations has greater ductility than other orientated specimens. The incipient plastic deformation and the stress-strain curves are presented and discussed for further understanding of the mechanical properties of single-crystal Al.
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  Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

  杨波, 李晓腾, 陈卫, 刘剑, 陈晓松

  理论物理通讯. 2016, 66(04): 439-446.

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  Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents ν, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model.
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  First-Principles Study of Structural, Magnetic, Electronic and Elastic Properties of PuC₂

  杨荣, 唐斌, 高涛, 敖冰云

  理论物理通讯. 2016, 66(04): 447-452.

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  We perform first-principles calculations of crystal structure, magnetism, electronic structure, chemical bonding and elastic properties for PuC₂ using the standard local spin-density approximation (LSDA)+U scheme. The use of the Hubbard term to describe the 5f electrons of plutonium is discussed according to the lattice parameters, magnetism and densities of states. Our calculated lattice constants and magnetism are in good agreement with the experimental data or other theoretical calculations. It is shown that the total densities of states at the Fermi energy level mainly come from the contribution of narrow f band. The Pu-C bonds of PuC₂ have a mixture of covalent character and ionic character, while covalent character is stronger than ionic character. The C1-C2 bonding has strong covalent character because of sp² hybridization between C atoms. Lastly, the elastic properties of PuC₂ are studied. We hope that our results can provide a useful reference for further theoretical and experimental research on PuC₂.
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  Effect of Misfit Strain on Pyroelectric Properties of (111) Oriented Pb(Zr_1-xTi_x)O₃ Thin Films

  邱建华, 陈智慧, 王秀琴, 袁宁一, 丁建宁

  理论物理通讯. 2016, 66(04): 453-458.

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  Based on the Landau-Dovenshire theory, the thermodynamic potential of (111) oriented films is constructed to investigate the pyroelectric properties of Pb(Zr_1-xTi_x)O₃ thin films. Due to the presence of nonlinear coupling terms resulted from the (111) epitaxy with substrates, the effects of misfit strain and electric field on the phase transitions at room temperature are more complex than that of (001) and (110) oriented films. Pb(Zr_0.5Ti_0.5)O₃ thin films with the Ti composition around the morphotropic phase boundary (MPB) have the giant dielectric and pyroelectric properties. Moreover, Pb(Zr_1-xTi_x)O₃ thin films grown on the tensile substrates which induce the triclinic γ phase have the larger dielectric and pyroelectric properties than that on the compressive substrates. Therefore, the physical properties of (111) oriented Pb(Zr_1-xTi_x)O₃ thin films can be adjusted by choosing the suitable substrates.
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  A Complex Network Model for Analyzing Railway Accidents Based on the Maximal Information Coefficient

  邵福波, 李克平

  理论物理通讯. 2016, 66(04): 459-466.

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  It is an important issue to identify important influencing factors in railway accident analysis. In this paper, employing the good measure of dependence for two-variable relationships, the maximal information coefficient (MIC), which can capture a wide range of associations, a complex network model for railway accident analysis is designed in which nodes denote factors of railway accidents and edges are generated between two factors of which MIC values are larger than or equal to the dependent criterion. The variety of network structure is studied. As the increasing of the dependent criterion, the network becomes to an approximate scale-free network. Moreover, employing the proposed network, important influencing factors are identified. And we find that the annual track density-gross tonnage factor is an important factor which is a cut vertex when the dependent criterion is equal to 0.3. From the network, it is found that the railway development is unbalanced for different states which is consistent with the fact.
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  Study of Friction between Liquid Crystals and Crystalline Surfaces by Molecular Dynamic Simulations

  张永文, 陈晓松, 陈卫

  理论物理通讯. 2016, 66(04): 467-473.

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  The lubrication characteristics of liquid crystal (LC) molecules sheared between two crystalline surfaces obtained from molecular dynamics (MD) simulations are reported in this article. We consider a coarse-grained rigid bead-necklace model of the LC molecules confined between two atomic surfaces subject to different shearing velocities. A systematic study shows that the slip length of LC lubrication changes significantly as a function of the LC-surface interaction energy, which can be well described though a theoretical curve. The slip length increases as shear rate increases at high LC-surface interaction energy. However, this trend can not be observed for low interaction energy. The orientation of the LC molecules near the surface is found to be guided by the atomics surfaces. The influence of temperature on the lubrication characteristics is also discussed in this article.
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  Relativistic Correction on Neutrino Emission from Neutron Stars in Various Parameter Sets

  丁文波, 戚湛强, 侯佳为, 密更, 特木尔巴根, 喻孜, 刘广洲, 赵恩广

  理论物理通讯. 2016, 66(04): 474-478.

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  In the relativistic mean field theory and cooling theories, relativistic correction on neutrino emission from neutron stars in four typical nuclear parameter sets, GM1, GL85, GPS250 and GPS300 is studied. Results show that relativistic effect makes the neutrino emissivity, neutrino luminosity and cooling rate lower, compared with the non-relativistic case. And the influence of relativistic effect grows with the mass of the neutron star. GPS300 set leads to the biggest fall in neutrino emissivity, whereas GM1 set leads to the largest disparity in cooling rate caused by relativistic effect.