2016年, 第66卷, 第03期　
刊出日期：2016-09-01

  

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  On Recursion Operator of the q-KP Hierarchy

  田可雷, 朱晓鸣, 贺劲松

  理论物理通讯. 2016, 66(03): 263-268.

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  It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy. The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.
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  Entropy, Fisher Information and Variance with Frost-Musulin Potenial

  J. O. A. Idiodi, C. A. Onate

  理论物理通讯. 2016, 66(03): 269-274.

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  This study presents the Shannon and Renyi information entropy for both position and momentum space and the Fisher information for the position-dependent mass Schrödinger equation with the Frost-Musulin potential. The analysis of the quantum mechanical probability has been obtained via the Fisher information. The variance information of this potential is equally computed. This controls both the chemical properties and physical properties of some of the molecular systems. We have observed the behaviour of the Shannon entropy. Renyi entropy, Fisher information and variance with the quantum number n respectively.
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  Fisher Information and Complexity Measure of Generalized Morse Potential Model

  C. A. Onate, J. O. A. Idiodi

  理论物理通讯. 2016, 66(03): 275-279.

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  The spreading of the quantum-mechanical probability distribution density of the three-dimensional system is quantitatively determined by means of the local information-theoretic quantity of the Shannon information and information energy in both position and momentum spaces. The complexity measure which is equivalent to Cramer-Rao uncertainty product is determined. We have obtained the information content stored, the concentration of quantum system and complexity measure numerically for n=0, 1, 2 and 3 respectively.
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  Multi-Party Quantum Private Comparison Protocol Based on Entanglement Swapping of Bell Entangled States

  叶天语

  理论物理通讯. 2016, 66(03): 280-290.

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  Recently, Liu et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57 (2012) 583). Subsequently, Liu et al. pointed out that in Liu et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62 (2014) 210). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, and then suggest the corresponding improvement by using the one-way hash function to encrypt the two users' secret inputs. We further put forward the three-party QPC protocol also based on entanglement swapping of Bell entangled state, and then validate its output correctness and its security in detail. Finally, we generalize the three-party QPC protocol into the multi-party case, which can accomplish arbitrary pair's comparison of equality among K users within one execution.
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  Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

  Shah Mohammad Bahauddin, Mir Mehedi Faruk

  理论物理通讯. 2016, 66(03): 291-296.

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  From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d=3 and d=2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d=1. This result suggests the equivalence between Bose and Fermi gases established in d=1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.
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  Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System

  李春来, 李文, 张敬, 谢元喜, 赵益波

  理论物理通讯. 2016, 66(03): 297-305.

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  A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar'e map, power spectrum, Kaplan-Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x₃ can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key.
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  Finite-Time Quasi-Synchronization of Two Nonidentical Chaotic Systems via Intermittent Control

  董燕, 咸进国

  理论物理通讯. 2016, 66(03): 306-314.

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  This paper investigates the finite-time quasi-synchronization of two nonidentical Lur'e systems with parameter mismatches by using intermittent control. Based on Lyapunov stability theory and some differential inequality techniques, sufficient conditions for finite-time quasi-synchronization are derived and the explicit expression of error level is obtained. Meanwhile, a numerical simulation is given to illustrate the effectiveness of the theoretical results.
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  Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

  İsmail Aslan

  理论物理通讯. 2016, 66(03): 315-320.

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  Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
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  Lie Symmetry Analysis, Conservation Laws and Exact Power Series Solutions for Time-Fractional Fordy-Gibbons Equation

  冯连莉, 田守富, 王秀彬, 张田田

  理论物理通讯. 2016, 66(03): 321-329.

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  In this paper, the time fractional Fordy-Gibbons equation is investigated with Riemann-Liouville derivative. The equation can be reduced to the Caudrey-Dodd-Gibbon equation, Savada-Kotera equation and the Kaup-Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.
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  Stationary Probability and First-Passage Time of Biased Random Walk

  李井文, 唐沈立, 徐新平

  理论物理通讯. 2016, 66(03): 330-334.

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  In this paper, we consider the stationary probability and first-passage time of biased random walk on 1D chain, where at each step the walker moves to the left and right with probabilities p and q respectively (0≤p, q≤1, p+q=1). We derive exact analytical results for the stationary probability and first-passage time as a function of p and q for the first time. Our results suggest that the first-passage time shows a double power-law F~(N-1)^γ, where the exponent γ=2 for N<|p-q|^-1 and γ=1 for N>|p-q|^-1. Our study sheds useful insights into the biased random-walk process.
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  Analysis of X(5568) as Scalar Tetraquark State in Diquark-Antidiquark Model with QCD Sum Rules

  王志刚

  理论物理通讯. 2016, 66(03): 335-339.

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  In this article, we take the X(5568) as the diquark-antidiquark type tetraquark state with the spin-parity J^P=0⁺, construct the scalar-diquark-scalar-antidiquark type current, carry out the operator product expansion up to the vacuum condensates of dimension-10, and study the mass and pole residue in details with the QCD sum rules. We obtain the value M_X=(5.57±0.12) GeV, which is consistent with the experimental data. The present prediction favors assigning the X(5568) to be the scalar tetraquark state.
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  A Three Higgs Doublet Model for Fermion Masses

  晁伟

  理论物理通讯. 2016, 66(03): 340-348.

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  In this paper we propose a possible explanation to the Fermion mass hierarchy problem by fitting the type-II seesaw mechanism into the Higgs doublet sector, such that their vacuum expectation values are hierarchal. We extend the Standard Model with two extra Higgs doublets as well as a spontaneously broken U_X(1) gauge symmetry. All the fermion Yukawa couplings except that of the top quark are of O(10^-2) in our model. Constraints on the parameter space of the model from low energy processes are studied. Besides, the lightest one of the neutral fermion fields, which is introduced to cancel the anomalies of the U(1)_X gauge symmetry can be the cold dark matter candidate. We investigate its signature in the dark matter direct detection.
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  Self-Focusing/Defocusing of Chirped Gaussian Laser Beam in Collisional Plasma with Linear Absorption

  Manzoor Ahmad Wani, Niti Kant

  理论物理通讯. 2016, 66(03): 349-354.

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  This paper presents an investigation on the self-focusing/defocusing of chirped Gaussian laser beam in collisional plasma with linear absorption. We have derived the differential equation for the beam width parameter by using WKB and paraxial approximations and solved it numerically. The effect of chirp and other laser plasma parameters is seen on the behavior of beam width parameter with dimensionless distance of propagation. The results are discussed and presented graphically. Our simulation results show that the amplitude of oscillations decreases with the distance of propagation. Due to collisional frequency, the laser beam shows fast divergence which can be minimized by the introduction of chirp parameter. The chirp decreases the effect of defocusing and increases the ability of self-focusing of laser beam in collisional plasma.
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  Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

  Xiao-Teng Li, Xiao-Song Chen

  理论物理通讯. 2016, 66(03): 355-362.

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  Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.
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  Abundance of Asymmetric Dark Matter in Brane World Cosmology

  Haximjan Abdusattar, Hoernisa Iminniyaz

  理论物理通讯. 2016, 66(03): 363-368.

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  Relic abundance of asymmetric Dark Matter particles in brane world cosmological scenario is investigated in this article. Hubble expansion rate is enhanced in brane world cosmology and it affects the relic abundance of asymmetric Dark Matter particles. We analyze how the relic abundance of asymmetric Dark Matter is changed in this model. We show that in such kind of nonstandard cosmological scenario, indirect detection of asymmetric Dark Matter is possible if the cross section is small enough which let the anti-particle abundance kept in the same amount with the particle. We show the indirect detection signal constraints can be used to such model only when the cross section and the 5-dimensional Planck mass scale are in appropriate values.