2012年, 第57卷, 第05期　
刊出日期：2012-05-15

  

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  Study of Exact Solutions to Cubic-Quintic Nonlinear Schrödinger Equation in Optical Soliton Communication

  刘彬, 阮航宇

  理论物理通讯. 2012, 57(05): 731-736.

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  A systematic method which is based on the classical Lie group reduction is used to find the novel exact solution of the cubic-quintic nonlinear Schrödinger equation (CQNLS) with varying dispersion, nonlinearity, and gain or absorption. Algebraic solitary-wave as well as kink-type solutions in three kinds of optical fibers represented by coefficient varying CQNLS equations are studied in detail. Some new exact solutions of optical solitary wave with a simple analytic form in these models are presented. Appropriate solitary wave solutions are applied to discuss soliton propagation in optical fibres, and the amplification and compression of pulses in optical fibre amplifiers.
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  Lie Symmetry Analysis, Bäcklund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations

  刘汉泽, 李继彬, 刘磊

  理论物理通讯. 2012, 57(05): 737-742.

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  This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations. All of the geometic vector fields of the equations are obtained, an optimal system of the equation is presented. Especially, the Bäcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry. Then, all of the symmetry reductions are provided in terms of the optimal system method, and the exact explicit solutions are investigated by the symmetry reductions and Bäcklund transformations.
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  Recursions in Calogero-Sutherland Model Based on Virasoro Singular Vectors

  吴剑锋, 续莺莺, 喻明

  理论物理通讯. 2012, 57(05): 743-758.

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  The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function, which is the spectrum generating function for the Calogero-Sutherland (CS) model. To accomplish this work, the hidden Virasoro structure in the CS model is much explored. In particular, we found that the Virasoro singular vectors form a skew hierarchy in the CS model. Literally, skew is analogous to coset, but here specifically refer to the operation on the Young tableaux. In fact, based on the construction of the Virasoro singular vectors, this hierarchical structure can be used to give a complete construction of the CS states, i.e. the Jack symmetric functions, recursively. The construction is given both in operator formalism as well as in integral representation. This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
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  Decay Mode Solutions for Kadomtsev-Petviashvili Equation

  樊国号, 邓淑芳, 张孟

  理论物理通讯. 2012, 57(05): 759-763.

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  The decay mode solutions for the Kadomtsev-Petviashvili (KP) equation are derived by Hirota method (direct method). The decay mode solution is a new set of analytical solutions with Airy function.
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  A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrödinger's Equation with Kerr Law Nonlinearity

  张再云, 甘向阳, 余德民, 张映辉, 李新平

  理论物理通讯. 2012, 57(05): 764-770.

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  In this paper, we investigate nonlinear the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity given in [Z.Y. Zhang, et al., Appl. Math. Comput. 216 (2010) 3064] and obtain exact traveling solutions by using infinite series method (ISM), Cosine-function method (CFM). We show that the solutions by using ISM and CFM are equal. Finally, we obtain abundant exact traveling wave solutions of NLSE by using Jacobi elliptic function expansion method (JEFEM).
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  Pairwise Quantum Correlations for Superpositions of Dicke States

  席政军, 熊恒娜, 李永明, 王晓光

  理论物理通讯. 2012, 57(05): 771-779.

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  Pairwise correlation is really an important property for multi-qubit states. For the two-qubit X states extracted from Dicke states and their superposition states, we obtain a compact expression of the quantum discord by numerical check. We then apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions, and the results are compared with those obtained by entanglement of formation, which is a quantum entanglement measure.
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  Cooperative Communications via Dual-Teleportation with Non-maximally Entanglement Measurements

  毛云, 郭迎, 曾贵华

  理论物理通讯. 2012, 57(05): 780-788.

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  We investigate a framework of the cooperative quantum teleportation (CQT) based on non-maximally entangled state basis (NB) measurements, instead of maximally entangled state basis (MB) measurements. It is implemented with two consecutive conventional (or direct) quantum telportations (DQT), where unknown quantum states can be transmitted in a point-to-point fashion. The security is based on the quantum-mechanical impossibility of local unitary transformations between non-maximally entangled states. It shows that the CQT can enhance the successful transmissions by self-correcting the errors introduced in the dual-teleportations.
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  Landau Damping of Collective Mode in a Quasi-One-Dimensional Repulsive Bose-Einstein Condensate

  杨占金, 柴兆亮, 李晨旭, 马晓栋

  理论物理通讯. 2012, 57(05): 789-794.

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  We investigate the Landau damping of the collective mode in a quasi-one-dimensional repulsive Bose-Einstein condensate by using the self-consistent time-dependent Hartree-Fock-Bogoliubov approximation. We put forward a new method to calculate the Landau damping rate of the collective mode in the condensate and discuss the dependence of the Landau damping on temperature, on transverse trapping frequency, on atom number in the condensate, and on length of the system. Different from the usual calculation method for the three dimension system, our new calculation method is an interactive one by considering the practical relaxation of the elementary excitation. With little approximation, our theoretical calculation results agree with the experimental ones. Comparing with the usual calculation method, our theory is helpful to deduce the inter-particle interactions in damping phenomenon.
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  Controlling Soliton Collisions of Condensates by Time-Dependence of Both Interactions and External Potential

  何章明, 王登龙, 丁建文, 颜晓红

  理论物理通讯. 2012, 57(05): 795-800.

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  Considering time-dependence of both interactions and external potential, we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation. It is found that for a closed external potential, the soliton-soliton distance is decreased with nonlinearly increased interactions, while the amplitude of each soliton increases and its width decreases. For linearly increased interactions but nonlinearly decreased external potential, especially, the atom transfer between two solitons is observed, different from previous theory of no atom transfer in solitons collision in a fixed external potential. In addition, it is shown that the collisional type, such as head-on,"chase", or collision period between two solitons, can be controlled by tuning both interactions and external potential. The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.
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  Flocking in Multi-Agent Systems with Multiple Virtual Leaders Based Only on Position Measurements

  苏厚胜

  理论物理通讯. 2012, 57(05): 801-807.

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  Most existing flocking algorithms assume one single virtual leader and rely on information on both relative positions and relative velocities among neighboring agents. In this paper, the problem of controlling a flock of mobile autonomous agents to follow multiple virtual leaders is investigated by using only position information in the sense that agents with the same virtual leader asymptotically attain the same velocity and track the corresponding virtual leader based on only position measurements. A flocking algorithm is proposed under which every agent asymptotically attains its desired velocity, collision between agents can be avoided, and the final tight formation minimizes all agents' global potentials. A simulation example is presented to verify and illustrate the theoretical results.
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  Adaptive Feedback Stabilization with Quantized State Measurements for a Class of Chaotic Systems

  王银河, 范永清, 王青云, 章云

  理论物理通讯. 2012, 57(05): 808-816.

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  We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states. The quantizer adopted in this paper takes finite many values. In particular, one zoomer is placed at the input terminal of the quantizer, and another zoomer is located at the output terminal of the quantizer. The zoomers possess a common adjustable time-varying parameter. By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization, the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems. Finally, some numerical examples are given to demonstrate the validity of the proposed methods.
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  Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

  李玉叶, 贾冰, 古华光, 安书成

  理论物理通讯. 2012, 57(05): 817-824.

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  Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.
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  Differential Operator Realization of the Exceptional Superalgebra D(2,1;α) and Its Application

  陈曦, 丁祥茂, 王晓辉, 杨文力

  理论物理通讯. 2012, 57(05): 825-832.

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  In this paper, we give the explicit expressions of the differential operator representations of the exceptional Lie superalgebra D(2,1;α). Based on these expressions, we construct free field realizations of the currents associated with D(2,1;α) at an arbitrary level k.
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  Mass of X(3872) in Bethe–Salpeter Equation for Quarks

  陈晓钊, 刘然慧, 石仁斌, 殷玉琴, 石宗华, 杨艾红, 吕晓夫

  理论物理通讯. 2012, 57(05): 833-840.

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  From Bethe–Salpeter equation, we deduce the equation which describes the two-body system consisting of a scalar meson and a vector meson. This equation is applied to investigate the exotic narrow state X(3872) assumed as a molecule state composed of D⁰D^*0. The contribution of the resonance D^-0 is the attractive interaction between two heavy mesons in this molecule state. The calculated mass of X is consistent with the experimental data.
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  Pole Analysis on Unitarized SU(3)× SU(3) One Loop χPT Amplitudes

  戴凌云, 王轩弓, 郑汉青

  理论物理通讯. 2012, 57(05): 841-848.

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  We analyze ππ-KK and πη-KK couple channel [1,1] matrix Padé amplitudes of SU(3)× SU(3) chiral perturbation theory. By fitting phase shift and inelasticity data, we determine pole positions in different channels (f₀(980), a₀(980), f₀(600), K₀^*(800), K^*(892), ρ(770)) and trace their N_c trajectories. We stress that a couple channel Breit-Wigner resonance should exhibit two poles on different Riemann sheets and meet each other on the real axis when N_c=∞. Poles are hence classified using this criteria and we conclude that K^*(892) and ρ(770) are unambiguous Breit-Wigner resonances. For scalars the situation is much less clear. We find that f₀(980) is a molecular state rather than a Breit-Wigner resonance, while a₀(980), though behave oddly when varying N_c, do maintain a twin pole structure.
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  Top Quark Pair Production via (un)Polarized Photon Collisions in the Littlest Higgs Model with T-parity at the ILC

  杨炳方

  理论物理通讯. 2012, 57(05): 849-854.

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  We study the top-quark pair production via polarized and unpolarized photon collisions at the International Linear Collider in the context of the littlest Higgs model with T-parity. We calculate the production cross section of the process γγ→tt and find the effects can be more significant in the (??) polarized photon collision mode than in other collision modes, and the relative correction can be expected to reach about ?1% in the favorable parameter space.
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  Interacting Theory of Chiral Bosons and Gauge Fields on Noncommutative Extended Minkowski Spacetime

  缪炎刚, 赵英杰

  理论物理通讯. 2012, 57(05): 855-865.

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  Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach.
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  Enhanced Cross-Phase Modulation via Phase Control in a Quantum dot Nanostructure

  郝向英, 郑安寿, 王英, 李小刚

  理论物理通讯. 2012, 57(05): 866-872.

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  A four-level quantum dot (QD) nanostructure interacting with four fields (two weak near-infrared (NIR) pulses and two control fields) forms the well-known double-cascade configuration. We investigate the cross-phase modulation (XPM) between the two NIR pulses. The results show, in such a closed-loop scheme, that the XPM can be greatly enhanced, while the linear absorption and two-photon absorption (gain) can be efficiently depressed by tuning the relative phase among the applied fields. This protocol may have potential applications in NIR all-optical switch design and quantum information processing with the solid-state materials.
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  Effect of Higher Order Axial Electron Temperature on Self-Focusing of Electromagnetic Pulsed Beam in Collisional Plasma

  夏雄平, 易林

  理论物理通讯. 2012, 57(05): 873-878.

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  Effect of higher order axial electron temperature on self-focusing of electromagnetic pulsed beam in collisional plasma is investigated. It is shown that higher order axial electron temperature T_p4 is not trivial than T_p0 and T_p2, which can modify slightly radial redistribution of electron density and increases effective dielectric constant. As a result, on one hand, slightly reduce electromagnetic beam self-focusing in the course of oscillatory convergence, on the other hand, quicken beam divergence in the course of steady divergence, i.e., higher order axial electron temperature T_p4 can decrease the influence of collisional nonlinearity in collisional plasma.
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  Nonlocal Free Energy of a Spatially Inhomogeneous Superconductor

  K.V. Grigorishin, B.I. Lev

  理论物理通讯. 2012, 57(05): 879-892.

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  The microscopic approach is developed for obtaining of the free energy of a superconductor based on direct calculation of the vacuum amplitude. The free energy functional of the spatially inhomogeneous superconductor in a magnetic field is obtained with help of the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of a magnetic response and the order parameter. Moreover, the nonlocality of the magnetic response is the consequence of order parameter's nonlocality. The extremals of this functional are considered in the explicit form in the low- and high-temperature limit at the condition of slowness of spatial variations of the order parameter.
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  Critical Properties of a Generalized Planar Rotator Model

  孙运周, 谭艳荣, 陈飞明

  理论物理通讯. 2012, 57(05): 893-896.

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  The critical properties of the planar rotator model with chiral Dzyaloshinsky-Moriya interaction are analyzed using a hybrid Monte Carlo method. Simulations on different lattices conform an observation that there is an XY-like Berezinskii-Kosterlitz-Thouless (BKT) phase transition in this model. The ground state and some thermodynamics properties are also discussed.
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  Evolution of Cooperation in Continuous Prisoner's Dilemma Games on Barabasi-Albert Networks with Degree-Dependent Guilt Mechanism

  王先甲, 全吉, 刘伟兵

  理论物理通讯. 2012, 57(05): 897-903.

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  This paper studies the continuous prisoner's dilemma games (CPDG) on Barabasi-Albert (BA) networks. In the model, each agent on a vertex of the networks makes an investment and interacts with all of his neighboring agents. Making an investment is costly, but which benefits its neighboring agents, where benefit and cost depend on the level of investment made. The payoff of each agent is given by the sum of payoffs it receives in its interactions with all its neighbors. Not only payoff, individual's guilty emotion in the games has also been considered. The negative guilty emotion produced in comparing with its neighbors can reduce the utility of individuals directly. We assume that the reduction amount depends on the individual's degree and a baseline level parameter. The group's cooperative level is characterized by the average investment of the population. Each player makes his investment in the next step based on a convex combination of the investment of his best neighbors in the last step, his best history strategies in the latest steps which number is controlled by a memory length parameter, and a uniformly distributed random number. Simulation results show that this degree-dependent guilt mechanism can promote the evolution of cooperation dramatically comparing with degree-independent guilt or no guilt cases. Imitation, memory, uncertainty coefficients and network structure also play determinant roles in the cooperation level of the population. All our results may shed some new light on studying the evolution of cooperation based on network reciprocity mechanisms.
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  Reachable Set Analysis for Dynamic Neural Networks with Polytopic Uncertainties

  左志强, 陈银萍, 王一晶

  理论物理通讯. 2012, 57(05): 904-908.

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  In this paper, the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties. The problem addressed here is to find a set as small as possible to bound the states starting from the origin by inputs with peak values. The maximal Lyapunov functional is proposed to derive a sufficient condition for the existence of a non-ellipsoidal bound to estimate the states of neural networks. It is theoretically shown that this method is superior to the traditional one based on the common Lyapunov function. Finally, two examples illustrate the advantages of our proposed result.