2015年, 第63卷, 第06期　
刊出日期：2015-06-01

  

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  Compatible Lie Bialgebras

  吴明忠, 白承铭

  理论物理通讯. 2015, 63(06): 653-664.

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  A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a "compatible version" of Lie bialgebras, that is, a pair of Lie bialgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the "compatible version" of the corresponding properties of Lie bialgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang-Baxter equation in compatible Lie algebras as a combination of two classical Yang-Baxter equations in Lie algebras. Furthermore, a notion of compatible pre-Lie algebra is introduced with an interpretation of its close relation with the classical Yang-Baxter equation in compatible Lie algebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang-Baxter equation given by Golubchik and Sokolov.
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  Solving the Generalized Higgs Model from the Generalized CRS Model

  宋词, 李艳, 陈景灵

  理论物理通讯. 2015, 63(06): 665-668.

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  In this paper, we reveal a direct relation between the generalized one-dimensional Carinena-Ranada-Santander (CRS) model and the radial part of two-dimensional generalized Higgs model. By this relation, we construct a series of quasi-exactly solutions for the two-dimensional Higgs model from a solved generalized CRS model.
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  Solutions and Continuum Limits of Two Semi-Discrete Lattice Potential Korteweg-de Vries Equations

  吴华, 潘佳佳, 张大军

  理论物理通讯. 2015, 63(06): 669-674.

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  We derive bilinear forms and Casoratian solutions for two semi-discrete potential Korteweg-de Vries equations. Their continuum limits go to the counterparts of the continuous potential Korteweg-de Vries equation.
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  Several Types of Similarity Solutions for the Hunter-Saxton Equation

  Mathew Baxter, Robert A. Van Gorder, Kuppalapalle Vajravelu

  理论物理通讯. 2015, 63(06): 675-681.

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  We study separable and self-similar solutions to the Hunter-Saxton equation, a nonlinear wave equation which has been used to describe an instability in the director field of a nematic liquid crystal (among other applications). Essentially, we study solutions which arise from a nonlinear inhomogeneous ordinary differential equation which is obtained by an exact similarity transform for the Hunter-Saxton equation. For each type of solution, we are able to obtain some simple exact solutions in closed-form, and more complicated solutions through an analytical approach. We find that there is a whole family of self-similar solutions, each of which depends on an arbitrary parameter. This parameter essentially controls the manner of self-similarity and can be chosen so that the self-similar solutions agree with given initial data. The simpler solutions found constitute exact solutions to a nonlinear partial differential equation, and hence are also useful in a mathematical sense. Analytical solutions demonstrate the variety of behaviors possible within the wider family of similarity solutions. Both types of solutions cast light on self-similar phenomenon arising in the Hunter-Saxton equation.
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  Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations

  孙国华, 董世海

  理论物理通讯. 2015, 63(06): 682-686.

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  Based on a Hamiltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchard-like (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary x^κ which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special κ in x^κ (κ ≥ 2). In particular, we find the orthogonal relation < n₁|n₂ >=δ_n1n2 (κ=0), < n₁|V'(x)|n₂ >=(E_n1-E_n2)²< n₁|x|n₂ > (κ=1), E_n=< n|V'(x)x/2|n >+< n|V(x)|n > (κ=2) and -4E_n< n|x|n >+< n|V'(x)x²|n > +4 < n|V(x)x|n >=0 (κ=3). The latter two formulas can be used directly to calculate the energy levels. We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
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  Uncertainty and Certainty Relations for Successive Projective Measurements of a Qubit in Terms of Tsallis' Entropies

  Alexey E. Rastegin

  理论物理通讯. 2015, 63(06): 687-694.

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  We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated after the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first-measurement state conditioned on the actual measurement outcome. Induced quantum uncertainties are characterized by means of the Tsallis entropies. For two successive projective measurement of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.
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  Coherent Destruction of Tunneling of Bosons with Effective Three-Body Interactions

  牛真霞, 鱼自发, 薛具奎

  理论物理通讯. 2015, 63(06): 695-700.

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  The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system.
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  f(T) Non-linear Massive Gravity and the Cosmic Acceleration

  吴悠, 陈祖成, 王家昕, 韦浩

  理论物理通讯. 2015, 63(06): 701-708.

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  Inspired by the f(R) non-linear massive gravity, we propose a new kind of modified gravity model, namely f(T) non-linear massive gravity, by adding the dRGT mass term reformulated in the vierbein formalism, to the f(T) theory. We then investigate the cosmological evolution of f(T) massive gravity, and constrain it by using the latest observational data. We find that it slightly favors a crossing of the phantom divide line from the quintessence-like phase (w_de > -1) to the phantom-like one (w_de < -1) as redshift decreases.
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  Quantization of Space in the Presence of a Minimal Length

  王伦舟, 龙超云, 隆正文

  理论物理通讯. 2015, 63(06): 709-714.

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  In this article, we apply the Generalized Uncertainty Principle (GUP), which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to αp³ (the result of the maximum momentum assumption) and α²p⁴ (the result of the minimum length assumption), where α ～ 1 / M_Plc is the GUP parameter. On the basis of the work by Ali et al., we solve the generalized Schrödinger equation which is extended to include the α² correction term, and find that the length L of the finite potential well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of α₀l_Pl in GUP scenario.
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  Minimal Length Effects on Schwinger Mechanism

  木本荣, 王鹏, 杨海棠

  理论物理通讯. 2015, 63(06): 715-720.

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  In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory (QFT) incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the deformed QFT. The same calculations are then performed in the case of Dirac particles. Finally, we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length.
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  Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

  吴红玉, 蒋黎红

  理论物理通讯. 2015, 63(06): 721-726.

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  A coupled variable-coefficient higher-order nonlinear Schrödinger equation in birefringent fiber is studied, and analytical multi-soliton, combined bright and dark soliton, W-shaped and M-shaped soliton solutions are obtained. Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed, and the decaying or increasing, even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.
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  Modified Kadomtsev-Petviashvili Equation in (3+1) Dimensions: Multiple Front-Wave Solutions

  A. M. Wazwaz, XU Gui-Qiong

  理论物理通讯. 2015, 63(06): 727-730.

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  A modified Kadomtsev-Petviashvili (mKP) equation in (3+1) dimensions is presented. We reveal multiple front-waves solutions for this higher-dimensional developed equation, and multiple singular front-wave solutions as well. The constraints on the coefficients of the spatial variables, that assure the existence of these multiple front-wave solutions are investigated. We also show that this equation fails the Painlevé test, and we conclude that it is not integrable in the sense of possessing the Painlevé property, although it gives multiple front-wave solutions.
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  Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrödinger-Boussinesq Equations

  乔丽静, 唐生强, 赵海霞

  理论物理通讯. 2015, 63(06): 731-742.

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  In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
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  Asymmetric Evolution of Two Two-Level Atoms Induced by Position-Dependent Excitation Phase

  周春晓, 张锐, 苏雪梅

  理论物理通讯. 2015, 63(06): 743-748.

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  We report a phenomenon of asymmetric evolution of two two-level atoms which results from pump laser phase based on the model of [Phys. Rev. Lett. 101 (2008) 153601]. Other than investigating the dynamical behavior of whole system, in this paper we investigate the effects of the pump laser phase on dynamic behavior of each atom. We find that two atoms show asymmetry both in time evolution of (population) excitation probability and quantum correlation with environment due to the quantum interference induced by pump laser phase as well as the dipole-dipole interaction. These phenomena are deeply related to the dynamical behavior of the whole system, therefore we can understand the dynamical behavior of whole system caused by pump laser phase from this point of view.
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  Evolution Properties of Atomic Fidelity in the Combined Multi-Atom-Cavity Field System

  王菊霞, 张晓娟, 张修兴

  理论物理通讯. 2015, 63(06): 749-753.

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  The atom fidelity is investigated in a system consisting of Mtwo-level atoms and M single-mode fields by use of complete quantum theory and numerical evaluation method. The influences of various system parameters on the evolution of atomic fidelity are studied. The results show that the atomic fidelity evolves in a Rabi oscillation manner. The oscillation frequency is mainly modulated by the coupling strength between atoms and light field, the atomic transition probabilities and the average photon numbers. Other factors hardly impact on the atomic fidelity. The present results may provide a useful approach to the maintenance of the atomic fidelity in the atom cavity field systems.
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  Electrostatic Nonplanar Positron-Acoustic Shock Waves in Superthermal Electron-Positron-Ion Plasmas

  M. J. Uddin, M. S. Alam, A. A. Mamun

  理论物理通讯. 2015, 63(06): 754-760.

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  The basic properties of the nonlinear propagation of the nonplanar (cylindrical and spherical) positron-acoustic (PA) shock waves (SHWs) in an unmagnetized electron-positron-ion (e-p-i) plasma containing immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated both analytically and numerically. The modified Burgers equation (mBE) is derived by using the reductive perturbation method. The basic features of PA SHWs are significantly modified by the cold positron kinematic viscosity (η), superthermal parameter of electrons (κ_e), superthermal parameter of hot positrons (κ_p), the ratio of the electron temperature to hot positron temperature (σ), the ratio of the electron number density to cold positron number density (μ_e), and the ratio of the hot positron number density to cold positron number density (μ_ph). This study could be useful to identify the basic properties of nonlinear electrostatic disturbances in dissipative space and laboratory plasmas.
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  A New Approach to Energy Integral for Investigation of Dust-Ion Acoustic (DIA) Waves in Multi-Component Plasmas with Quantum Effects in Inertia Less Electrons

  B. C. Kalita, R. Kalita

  理论物理通讯. 2015, 63(06): 761-768.

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  Dust-ion acoustic waves are investigated in this model of plasma consisting of negatively charged dusts, cold ions and inertia less quantum effected electrons with the help of a typical energy integral. In this case, a new technique is applied formulating a differential equation to establish the energy integral in case of multi-component plasmas which is not possible in general. Dust-ion acoustic (DIA) compressive and rarefactive, supersonic and subsonic solitons of various amplitudes are established. The consideration of smaller order nonlinearity in support of the newly established quantum plasma model is observed to generate small amplitude solitons at the decrease of Mach number. The growths of soliton amplitudes and potential depths are found more sensitive to the density of quantum electrons. The small density ratio r (=1-f) with a little quantized electrons supplemented by the dust charges Z_d and the in-deterministic new quantum parameter C₂ are found responsible to finally support the generation of small amplitude solitons admissible for the model.
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  First-Principles GGA+U Study of Intermediate-Band Characters from Zn_1-xM_xO (M=3d Transition-Metal) Alloys Suitable for High Efficiency Solar Cell

  吴孔平, 鲁开林, 蒋建彗, 顾书林, 汤琨, 叶建东, 朱顺明, 张荣, 郑有炓

  理论物理通讯. 2015, 63(06): 769-776.

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  The electronic structure characters are calculated for the Zn_1-xM_xO alloys with some Zn atoms in ZnO substituted by 3d transition-metal atoms (M), in order to find out which of these alloys could provide an intermediate band material used for fabricating high efficiency solar cell. Especially, among of these alloys, the electronic structure character and optical performance of Zn_1-xCr_xO alloys clearly show an intermediate band filled partially and isolated from the VB and the CB in energy band structure of ZnO host, and the intermediate band characters can be preserved with increasing Cr concentrations no more than 8.33% in Zn_1-xCr_xO alloys, at the same time, the ratio 0.52 of E_g^FC to E_g^VF in Zn_1-xCr_xO, (x=4.16%) alloy is closest to the optimal ratio of 0.57. Besides, compared to the ZnO, the optical absorption does indicate a great improved absorption below the calculated band gap of the ZnO and an enhancement of the optical absorption in the whole solar spectral energy range.
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  Magnetically Controlled Electronic Transport Properties of a Ferromagnetic Junction on the Surface of a Topological Insulator

  刘正钦, 王瑞强, 邓明勋, 胡梁宾

  理论物理通讯. 2015, 63(06): 777-782.

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  We have investigated the transport properties of the Dirac fermions through a ferromagnetic barrier junction on the surface of a strong topological insulator. The current-voltage characteristic curve and the tunneling conductance are calculated theoretically. Two interesting transport features are predicted: observable negative differential conductances and linear conductances tunable from unit to nearly zero. These features can be magnetically manipulated simply by changing the spacial orientation of the magnetization. Our results may contribute to the development of high-speed switching and functional applications or electrically controlled magnetization switching.