2015年, 第63卷, 第05期　
刊出日期：2015-05-01

  

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  Localized Properties of Rogue Wave for a Higher-Order Nonlinear Schrödinger Equation

  柳伟, 邱德勤, 贺劲松

  理论物理通讯. 2015, 63(05): 525-534.

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  In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higher-order nonlinear Schrödinger equation (HONLS) by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters α and β which denote the contribution of the higher-order terms (dispersions and nonlinear effects) included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
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  A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

  张玉峰, 吴立新, 芮文娟

  理论物理通讯. 2015, 63(05): 535-548.

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  With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated.
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  Construction of Soliton-Cnoidal Wave Interaction Solution for the (2+1)-Dimensional Breaking Soliton Equation

  程文广, 李彪, 陈勇

  理论物理通讯. 2015, 63(05): 549-553.

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  In this paper, the truncated Painlevé analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is difficult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus m=1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
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  An Alternative Adiabatic Quantum Algorithm for the Hamiltonian Cycle Problem

  张大剑, 仝殿民, 陆遥, 龙桂鲁

  理论物理通讯. 2015, 63(05): 554-558.

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  We put forward an alternative quantum algorithm for finding Hamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a von Neumann measurement on the final state, one may determine whether there is a Hamiltonian cycle in the graph and pick out a cycle if there is any. Although the proposed algorithm provides a quadratic speedup, it gives an alternative algorithm based on adiabatic quantum computation, which is of interest because of its inherent robustness.
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  Vector Meson Mass in Finite Density and Temperature Lattice QCD

  王睿, 陈莹, 宫明, 刘川, 刘玉斌, 刘朝峰, 马建平, 孟祥飞, 张剑波

  理论物理通讯. 2015, 63(05): 559-564.

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  Vector meson mass values are studied at finite chemical potential and temperature in lattice QCD with lattice size of 24×12²×6 using two flavors of staggered quarks. The investigation focuses on the change of the vector meson mass in the critical region close to T_c with two different types of chemical potentials switched on: the isoscalar chemical potential μS and its isovector counterpart μV. It is found that the vector meson mass increases in the QGP phase with both chemical potentials and decreases with μS in the confinement phase.
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  Modulational Instability of Spinor Condensates in an Optical Lattice

  郑公平, 简闻天, 杨玲玲

  理论物理通讯. 2015, 63(05): 565-568.

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  We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-one-dimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.
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  Superradiant Instability of D-Dimensional Reissner-Nordström Black Hole Mirror System

  李然, 赵俊坤, 张延明

  理论物理通讯. 2015, 63(05): 569-574.

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  We analytically study the superradiant instability of charged massless scalar field in the background of D-dimensional Reissner-Nordström (RN) black hole caused by mirror-like boundary condition. By using the asymptotic matching method to solve the Klein-Gordon equation that governs the dynamics of scalar field, we have derived the expressions of complex parts of boxed quasinormal frequencies, and shown they are positive in the regime of superradiance. This indicates the charged scalar field is unstable in D-dimensional Reissner-Nordström (RN) black hole surrounded by mirror. However, the numerical work to calculate the boxed quasinormal frequencies in this system is still required in the future.
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  Optimal Force Mismatch for Fluctuation-Activated Transition in a System of Two Coupled Bistable Oscillators

  陈含爽, 黄凤, 何刚, 申传胜, 侯中怀

  理论物理通讯. 2015, 63(05): 575-580.

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  We study the fluctuation-activated transition process in a system of two coupled forced bistable oscillators with a mismatch σ in the force constants. As the coupling strength μ is increased, the transition pathway undergoes four stages changes from a two-step process with two candidate pathways to a mixture of a two-step pathway and a one-step pathway to a one-step process with also two candidate pathways and then to a one-step process with a single pathway. Interestingly, we find that the total transition rate depends nonmonotonically on σ in the weak coupling: a maximal rate appears in an intermediate magnitude of σ. Moreover, the rate also exhibits an unexpected maximum as a function of μ. The results are in an excellent agreement with our numerical simulations by forward flux sampling.
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  Asymmetric Coupling in Two-Lane Asymmetric Simple Exclusion Processes with Unequal Injection Rates: Effect of Different Hoping Rates

  肖松, 陈晓瑜, 刘艳娜

  理论物理通讯. 2015, 63(05): 581-587.

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  This paper investigates the effect of both unequal injection rates and different hopping rates on two-lane asymmetric simple exclusion processes (ASEPs) with asymmetric coupling. When the hopping rates of both lanes are different, the system includes six steady phases, however, when the hopping rates of both lanes are same, the seventh phase (MC, MC) will exist in the system. Interestingly, with different hopping rates of both lanes, the densities of the system cannot be influenced by the non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte Carlo simulations.
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  Fast Generation of GHZ States with Bose-Einstein Condensate in a Cavity

  张刚, 周建, 薛正远

  理论物理通讯. 2015, 63(05): 588-590.

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  It is shown that strong coupling of Bose-Einstein condensates to an optical cavity can be realized experimentally. With an additional driven microwave field, we show that a highly nonlinear coupling among atoms in a Bose-Einstein condensate can be induced with the assistance of the cavity mode. With such interaction, we can investigate the generation of many body entangled states. In particularly, we show that multipartite entangled GHZ states can be obtained in such architecture with current available techniques.
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  Photo-Detached Electron Flux Distribution in a Gradient Electric Field

  王德华, 唐田田

  理论物理通讯. 2015, 63(05): 591-598.

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  This paper investigates the flux distributions of the electron photo-detached from H^- ion localized in a gradient electric field. In contrast with the photodetachment in the uniform electric field [Phys. Rev. A 40 (1989) 4983], where only two electron trajectories interfere at each given point on a detector, for the photodetachment in a gradient electric field, the electrons waves can travel along multiple paths from the negative ion to a given point on the detector plane, which makes the electron flux distributions on the detector plane become much complex. Using the semi-classical theory, we put forward a formula for calculating the electron flux. Our calculation results suggest that the electron flux distributions on a given detector plane is not only related to the propagation time of the detached electron, but also related to the detached electron's energy. With the increase of the detached electron's energy, the oscillating region in the electron flux distributions becomes enlarged and the oscillating structure in the flux distributions becomes much more complicated. This study will guide future experiment research on the photodetachment microscopy of the negative ions in the presence of non-uniform external fields.
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  High Efficiency Four-Wave Mixing with Relaxation Coupling of Longitude-Optical Phonons in Semiconductor Quantum Wells

  佘彦超, 郑学军, 王登龙, 丁建文

  理论物理通讯. 2015, 63(05): 599-604.

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  The time-dependent analysis of four-wave mixing (FWM) has been performed in four-level double semiconductor quantum wells (SQWs) considering the cross-coupling of the longitude-optical phonons (LOP) relaxation. It is shown that both the amplitude and the conversion efficiency of the FWM field enhance greatly with the increasing strength of cross-coupling of LOP relaxation. Interestingly, a double peak value of the conversion efficiency is obtained under a relatively weak single-photon detuning considering the LOP coupling. When the detuning becomes stronger, the double peaks turn into one peak appearing at the line respect to the about equality two control fields. The results can be interpreted by the effect of electromagnetically induced transparency and the indirect transition. Such controlled high efficiency FWM based on the cross-coupling LOP may have potential applications in quantum control and communications.
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  Nonautonomous Vortices in (2+1)-Dimensional Graded-Index Waveguide

  来娴静, 蔡晓鸥, 张解放

  理论物理通讯. 2015, 63(05): 605-612.

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  With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results.
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  Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

  安红利, 杨金晶, 阮文威

  理论物理通讯. 2015, 63(05): 613-618.

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  In this paper, the Clarkson-Kruskal direct approach is employed to investigate the exact solutions of the 2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2) and sech(kt/2) due to the rotational parameter k≠0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.
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  Molecular Dynamics Studies on Ballistic Thermal Resistance of Graphene Nano-Junctions

  姚文俊, 曹炳阳

  理论物理通讯. 2015, 63(05): 619-624.

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  Ballistic thermal resistance of graphene nano-junctions is investigated using non-equilibrium molecular dynamics simulation. The simulation system is consisted of two symmetrical trapezoidal or rectangular graphene nano-ribbons (GNRs) and a connecting nanoscale constriction in between. From the simulated temperature profile, a big temperature jump resulted from the constriction is found, which is proportional to the heat current and corresponds to a local ballistic thermal resistance. Fixing the constriction width and the length of GNRs, this ballistic thermal resistance is independent of the width of the GNRs bottom layer, i.e., the convex angle. But interestingly, this thermal resistance has obvious size effect. It is inversely proportional to the constriction width and will disappear with the constriction being wider. Moreover, based on the phonon dynamics theory, a theoretical model of the ballistic thermal resistance in two-dimensional nano-systems is developed, which gives a good explanation on microcosmic level and agrees well with the simulation result quantitatively and qualitatively.
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  Structural and Interaction Properties of Porphyrin Layers——A Quantum Chemical Study

  G. Praveena, A. Abiram

  理论物理通讯. 2015, 63(05): 625-634.

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  This paper is proposed to understand the interaction of porphyrin layers with diatomic molecules interacting at their interior regions by applying ab initio and density functional theory (DFT) methods. We have used NO, CO, and O₂ diatomic molecules to interact with the porphyrin layers. The most common Fe-centered metalloporphyrin structure with tetra-pyrrlic rings having N4 core is chosen for the study. The optimization of Porphyrin-Porphyrin (P_I-P_II) and Porphyrin-Diatomic molecule-Porphyrin (P_I-AB-P_II) (AB=NO, CO, and O₂) complexes are performed using HF method. In order to understand the planarity and appropriate stacking size of porphyrins and also to infer the separation of diatomic molecules between porphyrin layers the behavior of P_I-AB-P_II complexes (where AB=NO, CO, and O₂) are analyzed using structural properties and molecular electrostatic potentials (MEP). The MEPs are calculated using hybrid exchange correlation functional B3PW91 of DFT along with 6-31+G^* basis set for the P_I-P_II and P_I-AB-P_II complexes obtained from HF method.
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  Absorption Spectra and Refractive Index Changes of an Exciton in a Core/Shell Quantum Dot

  解文方

  理论物理通讯. 2015, 63(05): 635-640.

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  The absorption spectra and the refractive index changes are calculated theoretically for an exciton in a core/shell quantum dot. The advantage of our methodology is that one can investigate the influence of the repulsive core by varying two parameters in the confinement potential. The dimensionality effect of exciton quantum dots on the optical absorptions has been studied. It has been found that in the same regime, the optical absorption intensities of excitons are much smaller for the core/shell quantum dots than for the two-dimensional quantum rings. The linear and the nonlinear optical absorption coefficients and refractive index changes have been examined with the change of the confinement potential. The results show that the optical absorptions and the refractive index changes are strongly affected by the repulsive core of core/shell quantum dots. Moreover, the calculated results also reveal that as the inner radius increases, the peak values of the absorption coefficients and the refractive index changes of an exciton will show the optical Aharonov-Bohm oscillation in core/shell quantum dots.
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  Calculation of Half-Metal, Debye and Curie Temperatures of Co₂ VAl Compound: First Principles Study

  Arash Boochani, Heidar Khosravi, Jabbar Khodadadi, Shahram Solaymani, Masoud Majidiyan Sarmazdeh, Rohollah Taghavi Mendi, Sayed Mohammad Elahi

  理论物理通讯. 2015, 63(05): 641-647.

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  By FP-LAPW calculations, the structural, elastic, Debye and Curie temperatures, electronic and magnetic properties of Co₂VAl are investigated. The results indicate that Ferromagnetic (FM) phase is more stable than Anti-Ferromagnetic (AFM) and Non-magnetic (NM) ones. In addition, C₁₁-C₁₂ >0, C₄₄ >0, and B>0 so Co₂VAl is an elastically stable material with high Debye temperature. Also, the B/G ratio exhibits a ductility behavior. The relatively high Curie temperature provides it as a favorable material for spintronic application. It's electronic and magnetic properties are studied by GGA+U approach leading to a 100% spin polarization at Fermi level.
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  Cytoskeleton Dynamics: A Continuum Cooperative Hydrolysis Model

  胥建卫, 程波, 冯玉宇, 汪自庆, 王国栋

  理论物理通讯. 2015, 63(05): 648-652.

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  Cytoskeleton is a network of filamentous proteins, such as actin filaments and microtubules. We propose a continuum cooperative hydrolysis model which possesses exactly analytical solution to describe the dynamics of filament. The results show that the cooperativity leads to non negative-exponential distribution of T (ATP or GTP) subunits. As an application, we investigate the treadmilling phenomenon using our model. It is shown that the cooperativity remarkably affects the length of filament.