2016年, 第65卷, 第02期　
刊出日期：2016-02-01

  

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  Solutions to Class of Linear and Nonlinear Fractional Differential Equations

  Emad A-B. Abdel-Salam, Gamal F. Hassan

  理论物理通讯. 2016, 65(02): 127-135.

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  In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional KdV equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the (3+1)-space- time fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag-Leffler function methods. The obtained results recover the well-know solutions when α= 1.
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  Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

  Pierre Gaillard, Mickaël Gastineau

  理论物理通讯. 2016, 65(02): 136-144.

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  The Peregrine breather of order eleven (P₁₁ breather) solution to the focusing one-dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P₁₁ breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.
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  Basic and Fluctuating Periodic Instantons in Quantum Tunneling

  刘式适, 付遵涛, 刘式达, 赵强

  理论物理通讯. 2016, 65(02): 145-153.

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  Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lamé equation and their solutions are Lamé functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.
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  A Generalized Geometric Measurement of Quantum Discord: Exact Treatment

  崔海涛, 田俊龙, 杨癸

  理论物理通讯. 2016, 65(02): 154-164.

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  A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin-Meshkov-Glick and Dicke model.
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  Wave-Packet Collapse Based on Weak Repeatability or Covariant Condition

  吴照奇, 朱传喜, 王建辉

  理论物理通讯. 2016, 65(02): 165-168.

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  The conflict between the dynamics postulate (unitary evolution) and the measurement postulate (wave-packet collapse) of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys. Rev. A 76 (2007) 052110], and has further been extended to a more general scenario [Phys. Rev. A 87 (2013) 052111]. In this paper, we reconsider Zurek's new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.
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  Investigation of Bose Condensation in Ideal Bose Gas Trapped under Generic Power Law Potential in d Dimension

  Mir Mehedi Faruk, Md. Sazzad Hossain, Md. Muktadir Rahman

  理论物理通讯. 2016, 65(02): 169-176.

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  The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U =∑_i=1^d c_i|x_i/a_i|^n_i are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume C_V are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.
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  Consistent Riccati Expansion Method and Its Applications to Nonlinear Fractional Partial Differential Equations

  黄晴, 王丽真, 左苏丽

  理论物理通讯. 2016, 65(02): 177-184.

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  In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada-Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed.
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  Derivation of Mayer Series from Canonical Ensemble

  王先智

  理论物理通讯. 2016, 65(02): 185-188.

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  Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.
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  A Simple Structure for Signal Amplification

  丁万祥, 顾长贵, 梁晓明

  理论物理通讯. 2016, 65(02): 189-192.

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  It has been found that a triple-node feed-forward motif has a function of signal amplification, where two input nodes receive the external weak signal and jointly modulate the response of the third output node [Liang et al., Phys. Rev. E 88 (2013) 012910]. We here show that the signal amplification can be further enhanced by adding a link between the two input nodes in the feed-forward motif. We further reveal that the coupling strength of the link regulates the enhancement of signal amplification in the modified feed-forward motif. We finally analyze the mechanism of signal amplification of such simple structure.
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  A Proof of Factorization Theorem of Drell-Yan Process at Operator Level

  周高亮

  理论物理通讯. 2016, 65(02): 193-203.

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  An alternative proof of factorization theorem for Drell-Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed intoWilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines.
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  QCD Factorization of Semi-Inclusive DIS Process at Operator Level

  周高亮

  理论物理通讯. 2016, 65(02): 204-212.

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  The operator level proof of factorization theorem exhibited in [arXiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.
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  Parametrization of Barrier Characteristics for Spherical-Oblate Systems in any Configuration of Colliding Nuclei

  F. Lari, O. N. Ghodsi

  理论物理通讯. 2016, 65(02): 213-218.

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  The behaviors of barrier characteristics are analyzed for spherical-oblate systems over different configura- tions of colliding nuclei. For this purpose, we have extended our previous study [Phys. Rev. C 89 (2014) 054607], it is devoted to optimum “cold” and “hot” configuration] to analyze the same reaction systems in various configurations. The investigation on some chosen systems reveals that the barrier height and its position can be parameterized in times of the different orientations.
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  Photonic EPR State from Quadratic Waveguide Array with Alternating Positive and Negative Couplings

  杨莹, 徐平, 陆亮亮, 祝世宁

  理论物理通讯. 2016, 65(02): 219-224.

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  We propose the generation of photonic EPR state from quadratic waveguide array. Both the propagation constant and the nonlinearity in the array are designed to possess a periodical modulation along the propagation direction. This ensures that the photon pairs can be generated efficiently through the quasi-phase-matching spontaneous parametric down conversion by holding the spatial EPR entanglement in the fashion of correlated position and anticorrelated momentum. The Schmidt number which denotes the degree of EPR entanglement is calculated and it can approach a high value when the number of illuminated waveguide channels and the length of the waveguide array are properly chosen. These results suggest the quadratic waveguide array as a compact platform for engineering photonic quantum states in a high-dimensional Hilbert space.
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  Heisenberg Limit Phase Sensitivity in the Presence of Decoherence Channels

  Farzam Nosraty

  理论物理通讯. 2016, 65(02): 225-230.

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  In the present study, time evolution of quantum Cramer-Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.
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  Effects of Ellipticity Angle on Modulation Instabilities in Birefringent Optical Fibers

  李金花, 周国荣, 刘萍, 胡永正, 孙婷婷

  理论物理通讯. 2016, 65(02): 231-236.

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  Previous studies on modulation instabilities (MIs) in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle (0°≤θ≤ 90°). Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric (antisymmetric) CW states, we show that MI gain increases dramatically (reduces first and then enhances greatly) as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ= 45°, reappears across this ellipticity angle, and quickly increases after then.
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  Head-on Collision of Ion-acoustic Multi-Solitons in e-p-i Plasma

  Kaushik Roy, Malay Kumar Ghorui, Prasanta Chatterjee, Mouloud Tribeche

  理论物理通讯. 2016, 65(02): 237-246.

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  The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare-Lighthill-Kuo (PLK) method. Two different Kortewege-de Vries (K-dV) equations are derived. The Hirota's method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained.
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  Nonlinear Dust Acoustic Waves in Strongly Coupled Dusty Plasmas with Positively Charged Dust Particles

  王云良, 郭晓艳, 李泉水

  理论物理通讯. 2016, 65(02): 247-253.

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  The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation. We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev-Petviashvili (KP) equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.
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  Magneto-Transport and Nanomagnet Dynamics in MgO-Based Magnetic Tunnel Junctions (MTJs)

  Nader Ghobadi, Reza Daqiq

  理论物理通讯. 2016, 65(02): 254-258.

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  We investigate bias and different barrier thicknesses effects on quantities related to spin and charge currents in MgO-based magnetic tunnel junctions. Using the non-Equilibrium Green's function formalism, we demonstrate that the in-plane and out-of-plane components of the spin-transfer torque have asymmetric and symmetric behaviors respectively. Magneto-resistance also decreases with increasing barrier thickness. The Landau-Lifshits-Gilbert equation describes the dynamics of the magnetization made by spin transfer torque. Increasing in spin current above its critical value or smaller the magnet reduces the switching time which is major result for making of new memory devices.