2016年, 第66卷, 第02期　
刊出日期：2016-08-01

  

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  Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations

  刘汉泽, 辛祥鹏

  理论物理通讯. 2016, 66(02): 155-157.

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  This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
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  Universal Associated Legendre Polynomials and Some Useful Definite Integrals

  陈昌远, 尤源, 陆法林, 孙东升, 董世海

  理论物理通讯. 2016, 66(02): 158-162.

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  We first introduce the universal associated Legendre polynomials, which are occurred in studying the non-central fields such as the single ring-shaped potential and then present definite integrals I_A^±(a, τ)=∫_-1⁺¹x^a[P_l'^m'(x)]²/(1±x)^τdx, a=0, 1, 2, 3, 4, 5, 6, τ=1, 2, 3, I_B(b, σ)=∫_-1⁺¹x^b[P_l'^m'(x)]²/(1- x²)^σdx, b=0, 2, 4, 6, 8, σ=1, 2, 3, and I_C^±(c, κ)=∫_-1⁺¹x^c[P_l'^m'(x)]²/[(1-x²)^κ(1±x)]dx, c=0, 1, 2, 3, 4, 5, 6, 7, 8, κ=1, 2. The superindices “±” in I_A^±(a, τ) and I_C^±(c, κ) correspond to those of the factor (1±x) involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l' and m' are very useful and unavailable in classic handbooks.
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  Interaction Behaviours Between Solitons and Cnoidal Periodic Waves for (2+1)-Dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

  程雪苹, 王建勇, 任博, 杨云青

  理论物理通讯. 2016, 66(02): 163-170.

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  The consistent tanh expansion (CTE) method is employed to the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.
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  Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schrödinger Equations

  M. Asad-uz-zaman, H. Chachou Samet, U. Al Khawaja

  理论物理通讯. 2016, 66(02): 171-178.

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  We derive the Lax pairs and integrability conditions of the nonlinear Schrödinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrödinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrödinger equation.
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  Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev-Petviashvili Equation with Variable-Coefficient

  罗星雨, 陈勇

  理论物理通讯. 2016, 66(02): 179-188.

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  The extended form of modified Kadomtsev-Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation. Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation.
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  Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev-Petviashvili Equation

  黄丽丽, 陈勇, 马正义

  理论物理通讯. 2016, 66(02): 189-195.

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  A generalized Kadomtsev-Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev-Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev-Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.
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  Scattering States of l-Wave Schrödinger Equation with Modified Rosen-Morse Potential

  陈文利, 史艳维, 卫高峰

  理论物理通讯. 2016, 66(02): 196-200.

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  Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrödinger equation with the modified Rosen-Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.
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  Entanglement, Identical Particles and the Uncertainty Principle

  Gustavo Rigolin

  理论物理通讯. 2016, 66(02): 201-206.

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  A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.
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  On a Nonlinear Model in Adiabatic Evolutions

  孙杰, 路松峰

  理论物理通讯. 2016, 66(02): 207-210.

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  In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using.
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  Two Higgs Doublet Model III and Double-Lepton Polarization Asymmetries in ∧_b→∧μ⁺μ^- Decays

  王帅伟, 黄金书

  理论物理通讯. 2016, 66(02): 211-218.

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  Using the form factors calculated both in lattice QCD and HQET, we analyze the branching ratio, double- lepton polarization asymmetries and averaged double-lepton polarization asymmetries of ∧_b→∧μ⁺μ^- decay in the 2HDM III, respectively. Combining the experimental constrains on the 2HDM III parameters, we take two set of representative parameter spaces in our calculations. For the branching ratio of ∧_b→∧μ⁺μ^- decay, considering the uncertainties of the form factors and input parameters, we find the results of both SM and 2HDM III can satisfy the current experimental data in the framework of lattice QCD, but not in HQET. Then we calculate the double-lepton polarization asymmetries P_ij and their averaged values <P_ij>, we find the double-lepton polarization asymmetries P_LT, P_NN, and P_TT are sensitive to the 2HDM III. However, P_LN, P_NL, P_NT, and P_TN show the opposite results. The contribution of the 2HDM III to their averaged values have similar results.
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  Scalar Resonance at 750 GeV as Composite of Heavy Vector-Like Fermions

  廖玮, 郑汉青

  理论物理通讯. 2016, 66(02): 219-223.

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  We study a model of scalars which includes both the SM Higgs and a scalar singlet as composites of heavy vector-like fermions. The vector-like fermions are bounded by the super-strong four-fermion interactions. The scalar singlet decays to SM vector bosons through loop of heavy vector-like fermions. We show that the surprisingly large production cross section of di-photon events at 750 GeV resonance and the odd decay properties can all be explained. This model serves as a good model for both SM Higgs and a scalar resonance at 750 GeV.
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  Influence of Entropy on Composition and Structure of Massive Protoneutron Stars

  洪斌, 贾焕玉, 母雪玲, 周霞

  理论物理通讯. 2016, 66(02): 224-230.

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  Adjusting the suitable coupling constants in relativistic mean field (RMF) theory and focusing on thermal effect of an entropy per baryon (S) from 0 to 3, we investigate the composition and structure of massive protoneutron stars corresponding PSR J1614-2230 and PSR J0348+0432. It is found that massive protoneutron stars (PNSs) have more hyperons than cold neutron stars. The entropy per baryon will stiffen the equation of state, and the influence on the pressure is more obvious at low density than high density, while the influence on the energy density is more obvious at high density than low density. It is found that higher entropy will give higher maximum mass, higher central temperature and lower central density. The entropy per baryon changes from 0 to 3, the radius of a PNS corresponding PSR J0348+0432 will increase from 12.86 km to 19.31 km and PSR J1612-2230 will increase from 13.03 km to 19.93 km. The entropy per baryon will raise the central temperature of massive PNSs in higher entropy per baryon, but the central temperature of massive PNSs maybe keep unchanged in lower entropy per baryon. The entropy per baryon will increase the moment of inertia of a massive protoneutron star, while decrease gravitational redshift of a massive neutron star.
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  Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method

  A. Keshavarz, M. Naseri

  理论物理通讯. 2016, 66(02): 231-236.

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  In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps. Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.
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  Laser-Plasma Interaction in Presence of an Obliquely External Magnetic Field: Application to Laser Fusion without Radioactivity

  M. Mobaraki, S. Jafari

  理论物理通讯. 2016, 66(02): 237-243.

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  In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen-Boron (HB) fuel, the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle (from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.
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  Multiferroicity in Perovskite Manganite Superlattice

  陶永梅, 江学范, 刘俊明

  理论物理通讯. 2016, 66(02): 244-248.

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  Multiferroic properties of short period perovskite type manganite superlattice ((R₁MnO₃)_n/(R₂MnO₃)_n (n=1,2,3)) are considered within the framework of classical Heisenberg model using Monte Carlo simulation. Our result revealed the interesting behaviors in Mn spins structure in superlattice. Apart from simple plane spin cycloid structure which is shown in all manganites including bulk, film, and superlattice here in low temperature, a non-coplanar spiral spin structure is exhibited in a certain temperature range when n equals 1, 2 or 3. Specific heat, spin-helicity vector, spin correlation function, spin-helicity correlation function, and spin configuration are calculated to confirm this non-coplanar spiral spin structure. These results are associated with the competition among exchange interaction, magnetic anisotropy, and Dzyaloshinskii-Moriya interaction.
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  Containment Control for First-Order Multi-Agent Systems with Time-Varying Delays and Uncertain Topologies

  王付永, 杨洪勇, 张淑宁, 韩辅君

  理论物理通讯. 2016, 66(02): 249-255.

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  Containment control of first-order multi-agent systems with uncertain topologies and communication time-delays is studied. Suppose system topologies are dynamically changed, a containment control algorithm with time-varying delays is presented. The stability of the control algorithm is studied under the assumption that communication topologies are jointly-connected, and constraint condition of distributed containment control for delayed multi-agent systems is derived with the aid of Lyapunov-Krasovskii function. Simulation results are provided to prove the correctness and effectiveness of the conclusion.
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  Study of Tachyon Warm Intermediate and Logamediate Inflationary Universe from Loop Quantum Cosmological Perspective

  Jyotirmay Das Mandal, Ujjal Debnath

  理论物理通讯. 2016, 66(02): 256-262.

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  We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ=Γ₀ (where Γ₀ is a constant) in “intermediate” inflation and Γ=V(φ), (where V(φ) is the potential of tachyonic field) in “logamediate” inflation. We have assumed slow-roll condition to construct scalar field φ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained. We have analyzed the stability of this model through graphical representations.