2015年, 第63卷, 第01期　
刊出日期：2015-01-01

  

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  Two Hierarchies of New Differential-Difference Equations Related to the Darboux Transformations of the Kaup-Newell Hierarchy

  周汝光, 陈洁

  理论物理通讯. 2015, 63(01): 1-6.

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  Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup-Newell hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are studied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations.
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  CRE Method for Solving mKdV Equation and New Interactions Between Solitons and Cnoidal Periodic Waves

  焦向莉, 楼森岳

  理论物理通讯. 2015, 63(01): 7-9.

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  In nonlinear physics, the modified Korteweg de-Vries (mKdV) as one of the important equation of nonlinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion (CRE) method can unearth other equations.
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  Construction of Coarse-Grained Models by Reproducing Equilibrium Probability Density Function

  吕世靖, 周昕

  理论物理通讯. 2015, 63(01): 10-18.

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  The present work proposes a novel methodology for constructing coarse-grained (CG) models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as a functional of their equilibrium conformational probability densities, then is estimated from equilibrium averages of many independent physical quantities denoted as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from sufficiently preselected interesting physical quantities of the system. Thus the current method is named as probability density matching coarse-graining (PMCG) scheme, which effectively takes into account the overall characteristics of the original systems to construct CG model, and it is a natural improvement of the usual CG scheme wherein some physical quantities are intuitively chosen without considering their correlations. We verify the general PMCG framework in constructing a one-site CG water model from TIP3P model. Both structure of liquids and pressure of the TIP3P water system are found to be well reproduced at the same time in the constructed CG model.
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  An Enlarged Canonical Quantization Scheme and Quantization of a Free Particle on Two-Dimensional Sphere

  张中帅, 肖世发, 寻大毛

  理论物理通讯. 2015, 63(01): 19-24.

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  For a non-relativistic particle that freely moves on a curved surface, the fundamental commutation relations between positions and momenta are insufficient to uniquely determine the operator form of the momenta. With introduction of more commutation relations between positions and Hamiltonian and those between momenta and Hamiltonian, our recent sequential studies imply that the Cartesian system of coordinates is physically preferable, consistent with Dirac's observation. In present paper, we study quantization problem of the motion constrained on the two-dimensional sphere and develop a discriminant that can be used to show how the quantization within the intrinsic geometry is improper. Two kinds of parameterization of the spherical surface are explicitly invoked to investigate the quantization problem within the intrinsic geometry.
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  New Exact Solutions of Fractional Zakharov-Kuznetsov and Modified Zakharov-Kuznetsov Equations Using Fractional Sub-Equation Method

  S. Saha Ray, S. Sahoo

  理论物理通讯. 2015, 63(01): 25-30.

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  In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics;namely the space-time fractional Zakharov-Kuznetsov (ZK) and modified Zakharov-Kuznetsov (mZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann-Liouville sense.
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  On Hidden Symmetries of d>4 NHEK-N-AdS Geometry

  徐杰, 岳瑞宏

  理论物理通讯. 2015, 63(01): 31-35.

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  As well known, all higher dimensional Kerr-NUT-Ads metrics with arbitrary rotation and NUT parameters in an asymptotically AdS spacetime have a new hidden symmetry. In this paper, we show that in the near horizon, the isometry group is enhanced to include the dilatation and special conformal transformation, and find the conformal transformation contains the cosmological constant. It is demonstrated that for near horizon extremal Kerr-NUT-Ads (NHEK-N-AdS) only one rank-2 Killing tensor decomposes into a quadratic combination of the Killing vectors in terms of conformal group, while the others are functionally independent.
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  Two-Point Resistance of a Cobweb Network with a 2r Boundary

  谭志中, 方靖淮

  理论物理通讯. 2015, 63(01): 36-44.

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  We consider the problem of the two-point resistance on an m×n cobweb network with a 2r boundary, which has never been solved before. Up to now researchers just only solved the cases with free boundary or null resistor boundary. This paper gives the general formulae of the resistance between any two nodes in both finite and infinite cases using a method of direct summation pioneered by Tan [Z. Z. Tan, et al., J. Phys. A 46(2013)195202], which is simpler and can be easier to use in practice. This method contrasts the Green's function technique and the Laplacian matrix approach, which is difficult to apply to the geometry of a cobweb with a 2r boundary. We deduce several interesting results according to our general formula. In the end we compare and illuminate our formulae with two examples. Our analysis gives the result directly as a single summation, and the result is mainly composed of the characteristic roots.
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  Qubit Approach to the Topological Degeneracy of 4 and 6-Quasihole Pfaffian Paired Hall State

  崔海涛, 田俊龙, 杨癸

  理论物理通讯. 2015, 63(01): 45-50.

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  By virtue of the two-layer picture of Pfaffian pair Hall state, a qubit representation of topological degeneracy for quasiholes excitation is displayed. The non-Abelian feature of states can be manifested readily by the new wave functions. The virtue of this approach is that one does not need to find the equalities of Pfaffians, which is a so tedious task as exemplified for the case of six quasiholes. Then the braiding matrices are also constructed readily by just permutating single-qubit states, which are unitary and hermite.
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  Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

  刘爱洁, 郑连存, 马连喜, 张欣欣

  理论物理通讯. 2015, 63(01): 51-56.

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  In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker-Planck equation known as the Klein-Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function.
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  Periodic Wave, Solitary Wave and Compacton Solutions of a Nonlinear Wave Equation with Degenerate Dispersion

  朱文静, 陈爱永, 刘期怀

  理论物理通讯. 2015, 63(01): 57-62.

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  In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.
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  A Study of One S- and One P-Wave Heavy Meson Interaction in a Chiral Quark Model

  李明涛, 王文玲, 董宇兵, 张宗烨

  理论物理通讯. 2015, 63(01): 63-70.

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  The analytical forms of the interaction potentials between one pseudo-scalar/vector and one scalar/tensor/axial-vector heavy mesons are deduced based on a chiral quark model. Our results explicitly show the attractive property between the two heavy mesons. Consequently, a series of possible molecular states are obtained. It is expected that our study might shed some light on the popular discussions of the newly observed XYZ states.
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  All-Optical Switching between Optical Bistability and Multistability via Exciton Spin Relaxation

  Asadpour Seyyed Hossein, Rahimpour Soleimani Hamid

  理论物理通讯. 2015, 63(01): 71-76.

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  All-optical coherent control of optical bistability (OB) and optical multistability (OM) in the 4.8 nm ZnSe single-quantum well based on excitons and biexciton transitions is investigated. By applying a pair of phase-locked laser pulses all-optical coherent control can be obtained. Theoretical analysis with density matrix and Maxwell equations then yield the optical bistability and optical multistability. It is shown that by controlling the coherent and incoherent processes, the intensity threshold of OB and OM can be modified. Also, it is found that the switching between OB and OM or vice versa can be occurred for some controllable parameters.
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  An Exotic Phase Change in Dynamic Electrorheological Fluids

  黄俊樱, 李丛, 郑杰, 孟现文, 黄吉平, 周鲁卫

  理论物理通讯. 2015, 63(01): 77-85.

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  It is well known that constant or time-varying electric fields can induce phase changes in electrorheological (ER) fluids, from a liquid to semi-solid state, provided the field strength is larger than some critical value. We describe here an experimental and theoretical study considering yet a different class of phase changes, specifically those for an ER fluid in the presence of both shear flow and a time-varying electric field. We note that as the frequency of the field is decreased, the ER fluid will go from a liquid to an intermediate transition state, and eventually to a shear banding state. Our theoretical analysis further indicates that this phase change originates from competing effects of viscous and electrical forces. Ultimately, we conclude that it is possible to achieve various states and corresponding (desired) macroscopic properties of dynamic colloidal suspensions by adjusting the frequency of the externally applied electric field.
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  Extreme Ultraviolet Sources Generation by Using the Two-Color Multi-Cycle Weak Inhomogeneous Field

  冯立强, 李文亮

  理论物理通讯. 2015, 63(01): 86-90.

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  An efficient method for attosecond extreme ultraviolet source generation under the two-color multi-cycle weak pulse has been theoretically presented by using the concept of the plasmonic field enhancement in the vicinity of metallic nanostructures. The results show that by properly choosing the inhomogeneity of the two-color multi-cycle(20 fs)weak pulse(10¹³ W/cm²), not only the harmonic cutoff has been extended, resulting in a broadband XUV continuum, but also the single short quantum path has been selected to contribute to the harmonic. As a result, two isolated XUV pulses with durations of 68as and 66as can be obtained.
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  Lattice Boltzmann Simulation of Mixed Convection Heat Transfer in a Driven Cavity with Non-uniform Heating of the Bottom Wall

  Soufiene Bettaibi, Ezeddine Sediki, Frédéric Kuznik, Sauro Succi

  理论物理通讯. 2015, 63(01): 91-100.

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  The goal of this article is to study numerically the mixed convection in a differentially heated lid-driven cavity with non-uniform heating of the bottom wall. The velocity field is solved by a hybrid scheme with multiple relaxation time Lattice Boltzmann (MRT-LBM) model, while the temperature field is obtained by resolution of the energy balance equation using the finite difference method (FDM). First, the model is checked and validated using data from the literature. Validation of the present results with those available in the literature shows a good agreement. A good efficiency in time simulation is confirmed. Thereafter, the model has been applied to mixed convection in a driven cavity with non-uniform heating wall at the fixed Grashof number Gr=10⁶. It is found that, the heat transfer is weakened as the Richardson number is augmented. For Gr=10⁶, we note the appearance of secondary vortices at different positions of the cavity corners.
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  Phonon Excitation and Energy Redistribution in Phonon Space for Energy Dissipation and Transport in Lattice Structure with Nonlinear Dispersion

  徐志杰

  理论物理通讯. 2015, 63(01): 101-108.

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  We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics(MD)simulations. Locally dominant phonon modes(k-space)are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x,t)are critical to the concept of the local thermodynamic equilibrium(LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes(k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution(or frequency content)of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems. Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode(k=0)is excited first and gradually expanding to the highest mode(k_max(x,t), where k_max(x,t)can only asymptotically approach the maximum mode k^B of the first Brillouin zone(k_max(x,t→k^B). No energy distributed into modes with k_max(x, t) <k<k^B demonstrates that the local thermodynamic equilibrium cannot be established in harmonic chain. Energy is shown to be uniformly distributed in all available phonon modes k ≤k_max(x,t) at any position with heat transfer along the harmonic chain. The energy ux along the chain is shown to be a constant with time and proportional to the sound speed (ballistic transport).Comparison with the Fourier's law leads to a time-dependent thermal conductivity that diverges with time.
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  Conductance Spectra in Graphene-Superconductor Junctions

  田杰, 周世平, 邓振炎

  理论物理通讯. 2015, 63(01): 109-114.

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  The conductance spectra of a graphene ribbon and graphene-superconductor(G-S)junctions are investigated, using the tight-binding model and non-equilibrium Green's function formalism. It is found that the quantized conductance related to graphene's edge-states is robust against perturbations in the model parameters for a graphene monolayer ribbon with the zigzag boundary. With appropriate model parameter of the spin-orbit interaction strength, a new bound state with odd-frequency symmetry is found in the G-S junction. An enhancement in the zero-energy conductance amplitude is followed.
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  Code Optimization, Frozen Glassy Phase and Improved Decoding Algorithms for Low-Density Parity-Check Codes

  黄海平

  理论物理通讯. 2015, 63(01): 115-124.

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  The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check (bit) nodes have higher decoding thresholds compared to regular counterparts with homogeneous degree distribution. We also show that the instability of the mean-field calculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed (searching for the ground state), we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is close to the dynamical transition where all local search heuristics fail to identify the true message(codeword or the ferromagnetic state). After the dynamical transition, the number of metastable states with larger energy density (than the ferromagnetic state) becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentially numerous codewords sharing the identical ferromagnetic energy.