2017年, 第68卷, 第03期　
刊出日期：2017-09-01

  

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  Qubit Systems from Colored Toric Geometry and Hypercube Graph Theory

  Y. Aadel, A. Belhaj, M. Bensed, Z. Benslimane, M. B. Sedra, A. Segui

  理论物理通讯. 2017, 68(03): 285-289.

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  We develop a new geometric approach to deal with qubit information systems using colored graph theory. More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explored to attack qubit information problems using toric geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with CP¹, CP¹×CP¹ and CP¹×CP¹×CP¹ toric varieties respectively. Using a geometric procedure referred to as a colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of hypercube graph theory. Operations on toric information can produce universal quantum gates.
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  The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations

  趙天樂, 柳天陽, 陳曉寧, 周國榮

  理论物理通讯. 2017, 68(03): 290-294.

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  Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.
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  Lie Group Analysis and Invariant Solutions for Nonlinear Time-Fractional Diffusion-Convection Equations

  陈诚, 蒋耀林

  理论物理通讯. 2017, 68(03): 295-300.

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  On the basis of Lie group theory, (1+N)-dimensional time-fractional partial differential equations are studied and the expression of η_α⁰ is given. As applications, two special forms of nonlinear time-fractional diffusion-convection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.
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  A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrödinger-Boussinesq Equations Involving Riesz Fractional Derivative

  S. Saha Ray

  理论物理通讯. 2017, 68(03): 301-308.

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  In the present paper the Riesz fractional coupled Schrödinger-Boussinesq (S-B) equations have been solved by the time-splitting Fourier spectral (TSFS) method. This proposed technique is utilized for discretizing the Schrödinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.
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  New Metrics from a Fractional Gravitational Field

  Rami Ahmad El-Nabulsi

  理论物理通讯. 2017, 68(03): 309-312.

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  Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner-Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske-Kilbas-Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics.
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  Renormalization of Dirac Delta Potentials Through Minimal Extension of Heisenberg Algebra

  Fatih Erman

  理论物理通讯. 2017, 68(03): 313-316.

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  We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other regularization schemes given in the literature.
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  An Arbitrated Quantum Signature Scheme without Entanglement

  李慧然, 罗明星, 彭代渊, 王晓军

  理论物理通讯. 2017, 68(03): 317-322.

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  Several quantum signature schemes are recently proposed to realize secure signatures of quantum or classical messages. Arbitrated quantum signature as one nontrivial scheme has attracted great interests because of its usefulness and efficiency. Unfortunately, previous schemes cannot against Trojan horse attack and DoS attack and lack of the unforgeability and the non-repudiation. In this paper, we propose an improved arbitrated quantum signature to address these secure issues with the honesty arbitrator. Our scheme takes use of qubit states not entanglements. More importantly, the qubit scheme can achieve the unforgeability and the non-repudiation. Our scheme is also secure for other known quantum attacks.
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  Tunnelling Phenomenon near an Apparent Horizon in Two-Dimensional Dilaton Gravity

  曹利明, 姜小柱, 彭宇轩

  理论物理通讯. 2017, 68(03): 323-328.

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  Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon near the apparent horizon. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. By using the Hamilton-Jacobi method, the spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum. The temperature is proportional to the surface gravity of the apparent horizon as usual. Besides, in stationary cases we calculate the spectrum by using Parikh and Wilczek's null geodesic method and the result conforms to that obtained by using the Hamilton-Jacobi method. This is expected since the Hamilton-Jacobi method applies to generic spacetimes, including stationary ones.
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  On the Uniqueness of Ghost-Free Special Gravity

  柏栋, 邢宇航

  理论物理通讯. 2017, 68(03): 329-334.

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  Special gravity refers to interacting theories of massless gravitons in Minkowski space-time which are invariant under the abelian gauge invariance h_ab→h_ab+∂(_aχ_b) only. In this article we determine the most general form of special gravity free of Ostrogradski ghosts, meaning its equation of motion is of at most second order. Together with the recent works, this result could be helpful in formulating proofs of General Relativity as the unique physical theory of self-interacting massless gravitons. We also study how to construct gauge invariant couplings to matter fields.
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  Classification of Variational Conservation Laws of General Plane Symmetric Spacetimes

  Usamah S. Al-Ali, Ashfaque H. Bokhari, A. H. Kara, Ghulam Shabbir

  理论物理通讯. 2017, 68(03): 335-341.

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  In this article we discuss Noether conservation laws admitted by a Lagrangian L=g_ab(dx^a=ds)(dx^b=ds) of a test particle moving in the field of a general plane symmetric non-static spacetime metric. In this context, we first present a general solution representing a Noether symmetry vector subject to differential constraints satisfied by the general plane symmetric non-static metric. We then use a class of plane symmetric non-static metrics obtained by Feroze et al. and discuss, in each case, Noether conservation laws in comparison with Killing symmetries.
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  Quasi-Local Masses of Rotating Space-Times

  曾晓雄, 李玲

  理论物理通讯. 2017, 68(03): 342-346.

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  We derive the Misner-Sharp-like masses of the Reissner-Nordström black hole and the Einstein-Maxwell-Dilaton-Axion black hole by using the modified first law of thermodynamics. Their surface tensions are investigated. For the Reissner-Nordström black hole, the outer horizon radius is treated as a variable and the effective temperature is introduced. For the Einstein-Maxwell-Dilaton-Axion black hole, the outer horizon radius, the angular momentum unit mass and the parameter b are seen as three independent variables, and the mass, the horizon area and the angular momentum are functions of them.
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  Quantum Heat Engine and Negative Boltzmann Temperature

  席静怡, 全海涛

  理论物理通讯. 2017, 68(03): 347-356.

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  To clarify the ambiguity on negative Boltzmann temperature in literature, we study the Carnot and the Otto cycle with one of the heat reservoirs at the negative Boltzmann temperature based on a canonical ensemble description. The work extraction, entropy production and the efficiency of these cycles are explored. Conditions for constructing and properties of these thermodynamic cycles are elucidated. We find that the apparent "violation" of the second law of thermodynamics in these cycles are due to the fact that the traditional definition of thermodynamic efficiency is inappropriate in this situation. When properly understanding the efficiency and the adiabatic processes, in which the system crosses over "absolute ZERO" in a limit sense, the Carnot cycle with one of the heat reservoirs at a negative Boltzmann temperature can be understood straightforwardly, and it contradicts neither the second nor the third law of thermodynamics. Hence, negative Boltzmann temperature is a consistent concept in thermodynamics. We use a two-level system and an Ising spin system to illustrate our central results.
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  Time-Delay Effects on Constitutive Gene Expression

  冯燕陵, 董建敏, 王丹, 汤旭磊

  理论物理通讯. 2017, 68(03): 357-360.

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  The dynamics of constitutive gene expression with delayed mRNA degradation is investigated, where the intrinsic noise caused by the small number of reactant molecules is introduced. It is found that the oscillatory behavior claimed in previous investigations does not appear in the approximation of small time delay, and the steady state distribution still follows the Poisson law. Furthermore, we introduce the extrinsic noise induced by surrounding environment to explore the effects of this noise and time delay on the Fano factor. Based on a delay Langevin equation and the corresponding Fokker-Planck equation, the distribution of mRNA copy-number is achieved analytically. The time delay and extrinsic noise play similar roles in the gene expression system, that is, they are able to result in the deviation of the Fano factor from 1 evidently. The measured Fano factor for constitutive gene expression is slightly larger than 1, which is perhaps attributed to the time-delay effect.
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  Bond Dilution Effects on Bethe Lattice the Spin-1 Blume-Capel Model

  Erhan Albayrak

  理论物理通讯. 2017, 68(03): 361-365.

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  The bond dilution effects are investigated for the spin-1 Blume-Capel model on the Bethe lattice by using the exact recursion relations. The bilinear interaction parameter is either turned on ferromagnetically with probability p or turned off with probability 1-p between the nearest-neighbor spins. The thermal variations of the order-parameters are studied in detail to obtain the phase diagrams on the possible planes spanned by the temperature (T), probability (p) and crystal field (D) for the coordination numbers q=3, 4, and 6. The lines of the second-order phase transitions, T_c-lines, combined with the first-order ones, T_t-lines, at the tricritical points (TCP) are always found for any p and q on the (T, D)-planes. It is also found that the model gives only T_c-lines, T_c-lines combined with the T_t-lines at the TCP's and only T_t-lines with the consecutively decreasing values of D on the (T, p)-planes for all q.
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  Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control

  丁大为, 闫洁, 王年, 梁栋

  理论物理通讯. 2017, 68(03): 366-374.

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  In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective.
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  Dynamics of High-Order Spin-Orbit Couplings about Linear Momenta in Compact Binary Systems

  黄立, 伍歆, 梅丽杰, 黄国庆

  理论物理通讯. 2017, 68(03): 375-381.

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  This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian (3PN), 4PN, 5PN, 6PN and 7PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically.
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  A Derivation of the Entropy-Based Relativistic Smoothed Particle Hydrodynamics by Variational Principle

  Philipe Mota, 陈渭贤, 钱卫良

  理论物理通讯. 2017, 68(03): 382-386.

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  In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the fluid of high energy density but of low baryon density, the entropy is taken as the base quantity for the interpolation. The smoothed particle hydrodynamics algorithm employed in this study is of the second order, which guarantees better particle consistency. Furthermore, it is shown that the variational principle preserves the translational invariance of the system, and therefore improves the accuracy of the method. A brief discussion on the potential implications of the model in heavy ion physics as well as in general relativity are also presented.
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  Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

  Tasawar Hayat, Arsalan Aziz, Taseer Muhammad, Ahmed Alsaedi

  理论物理通讯. 2017, 68(03): 387-394.

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  The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.
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  Mechanical Anisotropic and Electronic Properties of Amm2-carbon under Pressure

  邢孟江, 李小珍, 余绍俊, 王付艳

  理论物理通讯. 2017, 68(03): 395-404.

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  Structural, electronic properties and mechanical anisotropy of Amm2-carbon are investigated utilizing first-principles calculations by Cambridge Serial Total Energy Package (CASTEP) code. The work is performed with the generalized gradient approximation in the form of Perdew-Burke-Ernzerhof (PBE), PBEsol, Wu and Cohen (WC) and local density approximation in the form of Ceperley and Alder data as parameterized by Perdew and Zunger (CA-PZ). The mechanical anisotropy calculations show that Amm2-carbon exhibit large anisotropy in elastic moduli, such as Poisson's ratio, shear modulus and Young's modulus, and other anisotropy factors, such as the shear anisotropic factor and the universal anisotropic index A^U. It is interestingly that the anisotropy in shear modulus and Young's modulus, universal anisotropic index and the shear anisotropic factor all increases with increasing pressure, but the anisotropy in Poisson's ratio decreases. The band structure calculations reveal that Amm2-carbon is a direct-band-gap semiconductor at ambient pressure, but with the pressure increasing, it becomes an indirect-band-gap semiconductor.