2016年, 第65卷, 第04期　
刊出日期：2016-04-01

  

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  Study on a General Hopf Hierarchy

  崔敏婕, 楼森岳

  理论物理通讯. 2016, 65(04): 393-396.

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  By using a general symmetry theory related to invariant functions, strong symmetry operators and hereditary operators, we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs. For the first order Hopf equation, there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions. The general solution of the first order Hopf equation is obtained via hodograph transformation. For the second order Hopf equation, the Hopf-diffusion equation, there are five sets of infinitely many symmetries. Especially, there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation. Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given.
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  Integrability and Solutions of the (2+1)-dimensional Hunter-Saxton Equation

  蔡红柳, 屈长征

  理论物理通讯. 2016, 65(04): 397-404.

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  In this paper, the (2+1)-dimensional Hunter-Saxton equation is proposed and studied. It is shown that the (2+1)-dimensional Hunter-Saxton equation can be transformed to the Calogero-Bogoyavlenskii-Schiff equation by reciprocal transformations. Based on the Lax-pair of the Calogero-Bogoyavlenskii-Schiff equation, a non-isospectral Lax-pair of the (2+1)-dimensional Hunter-Saxton equation is derived. In addition, exact singular solutions with a finite number of corners are obtained. Furthermore, the (2+1)-dimensional μ-Hunter-Saxton equation is presented, and its exact peaked traveling wave solutions are derived.
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  Singular 1-soliton and Periodic Solutions to the Nonlinear Fisher-Type Equation with Time-Dependent Coefficients

  Ozkan Guner, Ahmet Bekir

  理论物理通讯. 2016, 65(04): 405-409.

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  In this article, we establish exact solutions for the variable-coefficient Fisher-type equation. The solutions are obtained by the modified sine-cosine method and ansatz method. The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.
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  Addition Formulae of Discrete KP, q-KP and Two-Component BKP Systems

  高旭, 李传忠, 贺劲松

  理论物理通讯. 2016, 65(04): 410-422.

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  In this paper, we construct the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld-Sokolov hierarchies. With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies, we prove that these addition formulae are equivalent to these hierarchies. These studies show that the addition formula in the research of the integrable systems has good universality.
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  Quantification of Symmetry

  房一楠, 董国慧, 周端陆, 孙昌璞

  理论物理通讯. 2016, 65(04): 423-433.

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  Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking.
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  Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials

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

  理论物理通讯. 2016, 65(04): 434-440.

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  Non-relativistic phase shifts for a generalized Yukawa potential V(r)=-V₀(e^-αr/r)-V₁(e^-2αr/r²) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms. Small variations of V₁ seem to have marginal effects on the effective potential and on exact phase shifts. However, as pointed out in this study, a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts. The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.
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  Decomposition Properties of Quantum Discord

  Sunho Kim, 武俊德, Minhyung Cho

  理论物理通讯. 2016, 65(04): 441-446.

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  The quantum discord was introduced by Ollivier, Zurek, Henderson, and Vedral as an indicator of the degree of quantumness of mixed states. In this paper, we provide a decomposition condition for quantum discord. Moreover, we show that under the condition, the quantum correlations between the quantum systems can be captured completely by the entanglement measure. Finally, we present examples of our conclusions.
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  Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

  F. Siyouri, M. El Baz, S. Rfifi, Y. Hassouni

  理论物理通讯. 2016, 65(04): 447-452.

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  The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently. The authors [Phys. Rev. A 88 (2013) 034304] found that for some Bell-diagonal states (BDS) which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics, this phenomenon is known as the sudden change. Here in the present paper, we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs. Then, we find that basis change does not necessary mean sudden change of quantum correlations.
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  Dynamical Change of Quantum Fisher Information of Cavity-Reservoir Systems

  黄江, 谢钦

  理论物理通讯. 2016, 65(04): 453-459.

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  We study the quantum Fisher information (QFI) dynamics of the phase parameter in the enlarged cavity-reservoir systems at zero temperature under two situations of large N limit and non-Markovian environment, respectively. We find an important relation that the total quantities of QFI of the cavity and reservoir are equal to unit during the dynamical evolution. The lost QFI of the cavity transfers to its corresponding reservoir with the same quantities simultaneously. Moreover, we also find that the detuning parameter and non-Markovian effect are two significant factors to affect the preservation of QFI.
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  Multiple Multi-Qubit Quantum States Sharing

  秦华旺, 戴跃伟

  理论物理通讯. 2016, 65(04): 460-464.

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  A multiple multi-qubit quantum states sharing scheme is proposed, in which the dealer can share multiple multi-qubit quantum states among the participants through only one distribution and one recovery. The dealer encodes the secret quantum states into a special entangled state, and then distributes the particles of the entangled state to the participants. The participants perform the single-particle measurements on their particles, and can cooperate to recover the multiple multi-qubit quantum states. Compared to the existing schemes, our scheme is more efficient and more flexible in practice.
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  Energy Fluctuation of Ideal Fermi Gas Trapped under Generic Power Law Potential U=∑_i=1^dc_i|x_i/a_i|^n_i in d Dimensions

  Mir Mehedi Faruk, Md. Muktadir Rahman, Dwaipayan Debnath, Md. Sakhawat Hossain Himel

  理论物理通讯. 2016, 65(04): 465-468.

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  Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=∑_i=1^dc_i|x_i/a_i|^n_i has been calculated in arbitrary dimensions. Energy fluctuation is scrutinized further in the degenerate limit μ K_BT with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d=3 but also can describe the outcome for any power law potential in arbitrary dimension.
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  Massive Vector Particles Tunneling from the Neutral Rotating Anti-de Sitter Black Holes in Conformal Gravity

  李然, 赵俊坤

  理论物理通讯. 2016, 65(04): 469-472.

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  We investigate the massive vector particles' Hawking radiation from the neutral rotating Anti-de Sitter (AdS) black holes in conformal gravity by using the tunneling method. It is well known that the dynamics of massive vector particles are governed by the Proca field equation. Applying WKB approximation to the Proca equation, the tunneling probabilities and radiation spectrums of the emitted particles are derived. Hawking temperature of the neutral rotating AdS black holes in conformal gravity is recovered, which is consistent with the previous result in the literature.
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  Ground and Low-Lying Collective States of Rotating Three-Boson System

  Mohd. Imran, M. A. H. Ahsan

  理论物理通讯. 2016, 65(04): 473-482.

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  The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime. The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0≤L≤4N to obtain the ground and low-lying eigenstates. Our numerical results show that breathing modes with N-body eigenenergy spacing of 2?ω_⊥, known to exist in strictly 2D system with zero-range (δ-function) interaction potential, may as well exist in quasi-2D system with finite-range Gaussian interaction potential. To gain an insight into the many-body states, the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates. In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N≤(N-1) with q=2, 4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose-Laughlin like state. We further observe that the first breathing mode exhibits features similar to the Bose-Laughlin state in having eigenenergy, von Neumann entropy and internal structure independent of interaction for the three-boson system considered here. On the contrary, for eigenstates lying between the Bose-Laughlin like ground state and the first breathing mode, values of eigenenergy, von Neumann entropy and internal structure are found to vary with interaction.
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  Effects of f(R) Model on Dynamics of Axial Shear-Free Dissipative Fluids

  M. Sharif, Zunaira Nasir

  理论物理通讯. 2016, 65(04): 483-491.

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  We present a general analysis on non-static axial system with dissipative shear-free anisotropic fluid using polynomial inflationary f(R) model. We study the effects of dissipation on the dynamics of geodesic matter distribution. This leads the system either to rotation-free or expansion-free but not both simultaneously under geodesic condition. It is found that the system preserves its symmetry in both cases. For the rotation-free case, when there is no dissipation and Ricci scalar is constant, the axial system reduces to FRW universe model. This is exactly the same result obtained in general relativity.
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  F-theory and N=1 Quivers from Polyvalent Geometry

  Adil Belhaj, Moulay Brahim Sedra

  理论物理通讯. 2016, 65(04): 492-498.

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  We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-Kähler structure. Using intersecting complex toric surfaces, we derive a class of N=1 quivers with charged fundamental matter placed on external nodes. The emphasis is on how local Calabi-Yau equations solve the corresponding physical constraints including the anomaly cancelation condition. Concretely, a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.
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  Extending the MSSM with Singlet Higgs and Right Handed Neutrino for the Self-Interacting Dark Matter

  康海晶, 王雯宇

  理论物理通讯. 2016, 65(04): 499-505.

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  In order to meet the requirement of BBN, the right handed neutrino is added to the singlet Higgs sector in the GNMSSM. The spectrum and Feynman rules are calculated. the dark matter pheonomenology is also studied. In case of λ~0, the singlet sector can give perfect explanation of relic abundance of dark matter and small cosmological structure simulations. The BBN constraints on the light mediator can be easily solved by decaying to the right handed neutrino. When the λ_N is at the order of ο(0.1), the mass of the mediator can be constrained to several MeV.
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  Matter Effects on Neutrino Oscillations in Different Supernova Models

  徐晶, 胡立军, 李瑞成, 郭新恒, 杨炳麟

  理论物理通讯. 2016, 65(04): 506-516.

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  In recent years, with the development of simulations about supernova explosion, we have a better understanding about the density profiles and the shock waves in supernovae than before. There might be a reverse shock wave, another sudden change of density except the forward shock wave, or even no shock wave, emerging in the supernova. Instead of using the expression of the crossing probability at the high resonance, P_H, we have studied the matter effects on neutrino oscillations in different supernova models. In detail, we have calculated the survival probability of ν_e (P_s) and the conversion probability of ν_x (P_c) in the Schrödinger equation within a simplified two-flavor framework for a certain case, in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova. Our calculations was based on the data of density in three different supernova models obtained from simulations. In our work, we do not steepen the density gradient around the border of the shock wave, which differs to what was done in most of the other simulations. It is found that the mass and the density distribution of the supernova do make a difference on the behavior of P_s and P_c. With the results of P_s and P_c, we can estimate the number of ν_e (and ν_x) remained in the beam after they go through the matter in the supernova.
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  Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

  Tejal N. Shah, P. N. Gajjar

  理论物理通讯. 2016, 65(04): 517-522.

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  We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material, contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N→∞ . For the finite size, thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain. For the present 1D diatomic chain, obtained value of power divergent exponent of thermal conductivity 0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size, increases the thermal conductivity and existence of anomalous energy diffusion. Existing numerical data supports our findings.
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  Nonlinear Saturation Amplitude in Classical Planar Richtmyer-Meshkov Instability

  刘万海, 王翔, 蒋宏彬, 马文芳

  理论物理通讯. 2016, 65(04): 523-526.

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  The classical planar Richtmyer-Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh-Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI.
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  A Density Functional Theory Study of Codoping Characteristics of Sulfur with Alkaline Earth in Delafossite CuAlO₂

  刘其军, 秦涵, 刘正堂

  理论物理通讯. 2016, 65(04): 527-530.

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  The structural, electronic properties and formation energies of sulfur and alkaline earth codoped delafossite CuAlO₂ have been investigated using the first-principles density functional theory calculations. Our results reveal that the volume of codoping systems increases with the increasing atomic radius of metal atoms. The formation energies under different growth conditions have been calculated, showing that the codoping systems are formed easily under O-rich growth conditions. Electronic band structures and density of states have been obtained. The decreased bandgaps, enhanced covalence and appearance of electron acceptors after codoping are all good for p-type conductivity.
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  Positron-Electron Annihilation Process in (2,2)-Difluoropropane Molecule

  刘洋, 马晓光, 朱英浩

  理论物理通讯. 2016, 65(04): 531-537.

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  The positron-electron annihilation process in (2,2)-difluoropropane molecule and the corresponding gamma-ray spectra are studied by quantum chemistry method. The positrophilic electrons in (2,2)-difluoropropane molecule are found for the first time. The theoretical predictions show that the outermost 2s electrons of fluoride atoms play an important role in positron-electron annihilation process of (2,2)-difluoropropane. In the present scheme, the correlation coefficient between the theoretical gamma-ray spectra and the experiments can be 99%. The present study gives an alternative annihilation model for positron-electron pair in larger molecules.
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  Agegraphic Dark Energy with the Sign-Changeable Interaction in Non-Flat Universe

  徐友冬, 袁冬青

  理论物理通讯. 2016, 65(04): 538-542.

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  In this paper, we investigate the agegraphic dark energy (ADE) model by including the sign-changeable interaction between ADE and dark matter in non-flat universe. The interaction Q can change its sign from Q<0 to Q>0 as the universe expands. This indicates that at first dark matter decays to ADE, and then ADE decays to dark matter. We study the dynamical behavior of the model by using the phase-plane analysis. It is shown numerically that the coupling constant β plays an important role in the evolution of the universe. The equation of state (EoS) of ADE with the sign-changeable interaction is more likely to cross the phantom divide w_d=-1 from top to bottom with the increasing of the |β|. Whereas in ADE model with usual interaction, w_d can cross the phantom divide from bottom to top. We also find that our model is consistent with the observational data.