2018年, 第70卷, 第06期　
刊出日期：2018-12-01

  

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  Mixed Local-Nonlocal Vector Schrödinger Equations and Their Breather Solutions

  范蕊, 于发军

  理论物理通讯. 2018, 70(06): 651-660.

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  To the best of our knowledge, all nonlinearities in the known nonlinear integrable systems are either local or nonlocal. A natural problem is whether there exist some nonlinear integrable systems with both local and nonlocal nonlinearities, and how to solve this kinds of spectral nonlinear integrable systems with both local and nonlocal nonlinearities. Recently, some novel mixed local-nonlocal vector Schrödinger equations are presented, which are different from the single local and nonlocal coupled Schrödinger equation. We investigate the Darboux transformation of mixed local-nonlocal vector Schrödinger equations with a spectral problem. Starting from a special Lax pairs, the mixed localnonlocal vector Schrödinger equations are constructed. We obtain the one- and two- and N-soliton solution formulas of the mixed local-nonlocal vector Schrödinger equations with N-fold Darboux transformation. Based on the obtained solutions, the propagation and interaction structures of these multi-solitons are shown, the evolution structures of the one-solitons are exhibited, the overtaking elastic interactions among the two-breather solitons are considered. We find that unlike the local and nonlocal cases, the mixed local-nonlocal vector Schrödinger equations have some novel results. The results in this paper might be helpful for understanding some physical phenomena described in plasmas.
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  Circular Semi-Quantum Secret Sharing Using Single Particles

  叶崇强, 叶天语

  理论物理通讯. 2018, 70(06): 661-671.

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  Semi-quantum secret sharing (SQSS) is an important branch of semi-quantum cryptography, and differs from quantum secret sharing (QSS) in that not all parties are required to possess quantum capabilities. All previous SQSS protocols have three common features: (i) they adopt product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a tree-type way; and (iii) they require the classical parties to possess the measurement capability. In this paper, two circular SQSS protocols with single particles are suggested, where the first one requires the classical parties to possess the measurement capability while the second one does not have this requirement. Compared with the previous SQSS protocols, the proposed SQSS protocols have some distinct features: (i) they adopt single particles rather than product states or entangled states as initial quantum resource; (ii) the particles prepared by quantum party are transmitted in a circular way; and (iii) the second protocol releases the classical parties from the measurement capability. The proposed SQSS protocols are robust against some famous attacks from an eavesdropper, such as the measure-resend attack, the intercept-resend attack and the entangle-measure attack, and are feasible with present quantum technologies in reality.
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  Existence and Dynamics of Bounded Traveling Wave Solutions to Getmanou Equation

  温振庶

  理论物理通讯. 2018, 70(06): 672-676.

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  In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center, and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system.
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  Runaway Directions in O'Raifeartaigh Models

  孙铮, 卫星月

  理论物理通讯. 2018, 70(06): 677-682.

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  R-symmetries, which are needed for supersymmetry (SUSY) breaking in O’Raifeartaigh models, often lead to SUSY runaway directions trough a complexified R-transformation. Non-R symmetries also lead to runaway directions in a similar way. This work investigates the occurrence of runaway directions of both SUSY and SUSY breaking types. We clarify previous issues on fractional charges and genericness, and make a refined statement on conditions for runaway directions related to either R-symmetries or non-R symmetries. We present a generic and anomaly-free model to show the existence of runaway directions related to non-R symmetries. We also comment on the possibility to combine the non-R symmetry case to the R-symmetry case by an R-charge redefinition.
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  The 1/N_c Expansion in Hadron Effective Field Theory

  陈国英

  理论物理通讯. 2018, 70(06): 683-688.

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  We study the N_c scalings of pion-nucleon and nucleon-nucleon scatterings in hadron effective field theory. By assuming Witten's counting rules are applied to matrix elements or scattering amplitudes, which use the relativistic normalization for the nucleons, we find that the nucleon axial coupling g_A is of order N_c0, and a consistent large N_c counting can be established for the pion-nucleon and nucleon-nucleon scatterings. We also justify the nonperturbative treatment of the low energy nucleon-nucleon interaction with the large N_c analysis and find that the deuteron binding energy is of order 1=N_c.
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  Quasinormal Modes of the Planar Black Holes of a Particular Lovelock Theory

  文丹, 林凯, 钱卫良

  理论物理通讯. 2018, 70(06): 689-694.

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  In this work, we study the scalar quasinormal modes of a planar black hole metric in asymptotic anti-de Sitter spacetime derived from a particular Lovelock theory. The quasinormal frequencies are evaluated by adopting the Horowitz-Hubeny method as well as a matrix formalism. Also, the temporal evolution of small perturbations is studied by using finite difference method. The roles of the dimension of the spacetime, the parameter of the metric k, as well as the temperature of the background black hole, are discussed. It is observed that the particular form of the metric leads to quasinormal frequencies whose real parts are numerically insignificant. The black hole metric is found to be stable against small scalar perturbations.
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  Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity

  梁钧

  理论物理通讯. 2018, 70(06): 695-704.

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  The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases. Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η, (l, n), ∈ and N_q, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.
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  Collective Diffusion and Strange-Metal Transport

  杜林鹏, 吴绍锋, 杨国宏

  理论物理通讯. 2018, 70(06): 705-712.

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  We study a particular combination of charge and heat currents, which is decoupled with the heat current. The "heat-decoupled" (HD) current can be transported by diffusion at long distances, when the thermoelectric effect is small, large, or balanced. Using holographic models with momentum relaxation, we illustrate that the different thermoelectric effects correspond to the high temperatures and strong disorder, low temperatures, or special critical index. Meanwhile, the Einstein-like relation and the diffusion/chaos relation may be emergent. Assuming that the existence and features of HD modes appear in strange metals, we can predict that when the thermoelectric effect is not very large, the scaling of resistivity is predominantly controlled by the HD susceptibility and chaos; otherwise more physics is required.
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  A Pressure Parametric Dark Energy Model

  王俊超, 孟新河

  理论物理通讯. 2018, 70(06): 713-720.

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  In this paper, we propose a new pressure parametric model of the total cosmos energy components in a spatially flat Friedmann-Robertson-Walker (FRW) universe and then reconstruct the model into quintessence and phantom scenarios, respectively. By constraining with the datasets of the type Ia supernova (SNe Ia), the baryon acoustic oscillation (BAO) and the observational Hubble parameter data(OHD), we find that Ω_m0=0.270_-0.034^+0.039 at the 1σ level and our universe slightly biases towards quintessence behavior. Then we use two diagnostics including Om(a) diagnostic and statefinder to discriminate our model from the cosmology constant cold dark matter (ΛCDM) model. From Om(a) diagnostic, we find that our model has a relatively large deviation from the ΛCDM model at high redshifts and gradually approaches the ΛCDM model at low redshifts and in the future evolution, but they can be easily differentiated from each other at the 1σ level all along. By the statefinder, we find that both of quintessence case and phantom case can be well distinguished from the ΛCDM model and will gradually deviate from each other. Finally, we discuss the fate of universe evolution (named the rip analysis) for the phantom case of our model and find that the universe will run into a little rip stage.
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  Testing Photons Coupled to Weyl Tensor with Gravitational Time Advancement

  李刚, 邓雪梅

  理论物理通讯. 2018, 70(06): 721-727.

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  Classical Solar System tests of photons coupled to Weyl tensor with two polarizations were studied in a recent work. A coupling strength parameter α in this model was firstly obtained as |α|<4×10¹¹ m² by using available datasets in the Solar System. In this paper, a new test called by gravitational time advancement is proposed and investigated to test such the coupling. This new test, which is quite different from Shapiro time delay, depends strongly on round-trip proper time span (not coordinate time one) of flight of radio pulses between an observer on the Earth and a distant spacecraft. For ranging a spacecraft getting far away from the Sun, two special cases (the superior/inferior conjunctions) are used to analyse the observability in the advancement contributed by the Weyl coupling. We found that the situation of the inferior conjunction is more suitable for detecting the advancement caused by such the Weyl coupling. In either case, two kinds of polarizations make the advancement in the model smaller or larger than the one of general relativity. Although the observability in the advancement could be out of the reach of already existing technology, the implement of planetary laser ranging and optical clocks might provide us more insights on such the Weyl coupling in the near future.
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  Data-Based Optimal Bandwidth for Kernel Density Estimation of Statistical Samples

  李振伟, 何平

  理论物理通讯. 2018, 70(06): 728-734.

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  It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples, since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%~3% for sample size larger than 10⁴. This approach can also be generalized easily to cases of variable kernel estimations.
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  GWs from S-stars Revolving Around SMBH at Sgr A*

  蔡荣根, 刘同波, 王少江

  理论物理通讯. 2018, 70(06): 735-748.

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  A preliminary estimation of gravitational waves (GWs) from the extreme-mass-ratio-inspirals (EMRIs) system in the Galactic Centre (GC) is given for the 37 observed S-stars revolving around the supermassive black hole (SMBH) at Sagittarius (Sgr) A^*. Within this century, the total strain of the gravitational waveform calculated from the post-Newtonian (PN) method with eccentricity is well below the current planned sensitivity of pulsar-timing-array (PTA). New technology might be required in order to extract GW signal from this EMRIs system for future PTA detections.
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  Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference

  李鹏飞, 乔丽颜, 赵叶华, 陈江星, 马军

  理论物理通讯. 2018, 70(06): 749-752.

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  The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.
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  Path of Momentum Integral in the Skorniakov-Ter-Martirosian Equation

  高超, 张芃

  理论物理通讯. 2018, 70(06): 753-758.

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  The Skorniakov-Ter-Martirosian (STM) integral equation is widely used for the quantum three-body problems of low-energy particles (e.g., ultracold atom gases). With this equation these three-body problems can be efficiently solved in the momentum space. In this approach the boundary condition for the case that all the three particles are gathered together is described by the upper limit of the momentum integral, i.e., the momentum cutoff. On the other hand, in realistic systems, the three-body recombination (TBR) process can occur when all these three particles are close to each other. In this process two particles form a deep dimer and the other particle can gain high kinetic energy and then escape from the low-energy system. In the presence of the TBR process, the momentum-cutoff in the STM equation would include a non-zero imaginary part. As a result, the momentum integral in the STM equation should be done in the complex-momentum plane. In this case the result of the integral depends on the choice of the integral path. Obviously, only one integral path can lead to the correct result. In this paper we consider how to correctly choose the integral path for the STM equation. We take the atom-dimer scattering problem in a specific ultracold atom gas as an example, and show the results given by different integral paths. Based on the result for this case we explore the reasonable integral paths for general case.
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  Sine-Gordon Solitons and Breathers in Rod-like Magnetic Liquid Crystals under External Magnetic Field

  李妍, 鲁小波, 侯春风

  理论物理通讯. 2018, 70(06): 759-764.

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  To study the nonlinear phenomena in rod-like magnetic liquid crystals (RMLCs), this paper establishes the dynamic model of molecular motion when giving a twisting disturbance to the molecules under external magnetic field. We find the twist of the molecules under magnetic field can be propagated in the form of a traveling wave. The dynamic equation of the molecular twisting we derived satisfies the form of Sine-Gordon equation. We obtain two solutions of the Sine-Gordon equation by theoretical calculation: the kink and anti-kink solitons and breathers. The characteristics of those solitons and breathers are discussed.
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  Dipole Polarizabilities of the Ground States for Berylliumlike Ions

  陈超, 苟秉聪

  理论物理通讯. 2018, 70(06): 765-770.

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  Dipole polarizabilities of the ground states for berylliumlike ions with nuclear charge Z = 4 to 10 are calculated by using the Rayleigh-Ritz variational method with multiconfiguration interaction wave functions. The representative models of convergence are listed and compared with other theoretical data for nuclear charge Z = 4 to 6. The present dipole polarizabilities are in good agreement with previous accurate theoretical values available in the literature. For results with greater nuclear charge number, the present calculations may provide benchmarked data for future theoretical and experimental studies. Dynamic dipole polarizabilities of the ground state for the beryllium atom at selected frequencies are also calculated and compared with other theoretical values in the literature.
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  Ratio Between Sensitive Strength to Light Information and Coupling Strength Affects Entrainment Range of Suprachiasmatic Nucleus

  顾长贵, 杨会杰, 王曼

  理论物理通讯. 2018, 70(06): 771-776.

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  The suprachiasmatic nucleus (SCN), an endogenous clock in the brain of the mammals, regulates the physiological and behavioral activities according to the natural 24 h light-darkness cycle. Animals can also entrain themselves to non 24 h light-darkness cycles. The range of the periods which the animal can entrain to is called entrainment range. Previous studies have found that the entrainment range depends on the coupling strength and the sensitive strength to the light for the SCN neurons. However, the effect of the interplay between these two strengths on the entrainment range has not been examined. In the present study, we examine the effect of the ratio of the sensitive strength to the coupling strength on the entrainment range. We find that there is a parabolic-like relationship between the entrainment range and the ratio, and the largest entrainment range is obtained with a suitable ratio. Interestingly, the value of this suitable ratio is related to the comparison in the intrinsic amplitudes between the light information sensitive neurons and the light information insensitive neurons. Our finding will shed light on the interplay between the sensitive strength to the light information and the coupling strength, and the understanding for the diversity of the entrainment range among various species.
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  Analysis of Melting Heat Transport in a Cross Flow Direction: A Comparative Study

  G. K. Ramesh, S. A. Shehzad

  理论物理通讯. 2018, 70(06): 777-784.

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  An incompressible three-dimensional laminar flow in a cross flow direction is described in this work. The term of melting and viscous dissipation is incorporated in the mathematical modeling of present flow problem. The flow expressions are converted into dimensionless equations, which are solved with help of Runge-Kutta scheme. Impact of the emerging parameters on the non-dimensional velocities and temperature and friction-factors and local Nusselt number are examined. The convergence analysis is found for ∈ < 0 and 0 < ∈ ≤ 2. Comparative analysis is made between the obtained results and published data for limiting case. It is explored at the surface that the melting parameter retards the liquid temperature while it enhances the fluid velocity.
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  Directed Dominating Set Problem Studied by Cavity Method: Warning Propagation and Population Dynamics

  玉素甫·艾比布拉

  理论物理通讯. 2018, 70(06): 785-794.

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  The minimal dominating set for a digraph (directed graph) is a prototypical hard combinatorial optimization problem. In a previous paper, we studied this problem using the cavity method. Although we found a solution for a given graph that gives very good estimate of the minimal dominating size, we further developed the one step replica symmetry breaking theory to determine the ground state energy of the undirected minimal dominating set problem. The solution space for the undirected minimal dominating set problem exhibits both condensation transition and cluster transition on regular random graphs. We also developed the zero temperature survey propagation algorithm on undirected Erdös-Rényi graphs to find the ground state energy. In this paper we continue to develope the one step replica symmetry breaking theory to find the ground state energy for the directed minimal dominating set problem. We find the following. (i) The warning propagation equation can not converge when the connectivity is greater than the core percolation threshold value of 3.704. Positive edges have two types warning, but the negative edges have one. (ii) We determine the ground state energy and the transition point of the Erdös-Rényi random graph. (iii) The survey propagation decimation algorithm has good results comparable with the belief propagation decimation algorithm.
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  A Class of Rumor Spreading Models with Population Dynamics

  董苏雅拉图, 黄永畅

  理论物理通讯. 2018, 70(06): 795-802.

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  Based on the characteristics of rumor spreading in online social networks, this paper proposes a new rumor spreading model. This is an improved SIS rumor spreading model in online social networks that combines the transmission dynamics and population dynamics with consideration of the impact of both of the changing number of online social network users and different levels of user activity. We numerically simulate the rumor spreading process. The results of numerical simulation show that the improved SIS model can successfully characterize the rumor spreading behavior in online social networks. We also give the effective strategies of curbing the rumor spreading in online social networks.
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  New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

  彭光含, 阳树洪, 赵红专

  理论物理通讯. 2018, 70(06): 803-807.

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  A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.
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  Super-sensitivity in Dynamics of Ising Model with Transverse Field: From Perspective of Franck-Condon Principle

  徐磊, 杨立平

  理论物理通讯. 2018, 70(06): 808-816.

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  We study the role of Franck-Condon (F-C) principle in the dynamics of a central spin system, which is coupled to an Ising chain in transverse field. The transition process of energy levels caused by the excited central spin is studied to manifest the quantum critical effect through the Franck-Condon principle. The super-sensitivity of this quantum critical system is demonstrated clearly from the properties of Franck-Condon factors. We analytically show how spin numbers, coupling strength and order parameter of the Ising chain sensitively effect on the energy level populations in dynamical evolution near the critical point. This super-sensitivity and criticality are explicitly displayed in absorption spectrum.
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  On the Singular Effects in the Relativistic Landau Levels in Graphene with a Disclination

  Rosinildo F. do Nascimento, Diego Cogollo, Edilberto O.Silva, Moisés Rojas, Cleverson Filgueiras

  理论物理通讯. 2018, 70(06): 817-822.

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  The effect of a pseudo Aharonov-Bohm (AB) magnetic field generated by a disclination on a two-dimensional electron gas in graphene is addressed in the continuum limit within the geometric approach. The influence of the coupling between the spinor fields and the singular conical curvature is investigated, which shows that singularities have pronounced impact in the Hall conductivity. Moreover, the degeneracy related to the Dirac valleys is broken for negative values of the angular momentum quantum numbers, l, including l ≡ 0. In this case, a Hall plateau develops at the null filling factor. Obtaining the Hall conductivity by summing over the positive and the negative l's, the null Landau level is recovered and the plateau at the null filling factor disappears. In any case, the standard plateaus, which are seen in a flat graphene are not obtained with these curvature and singular effects.
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  Magnetic Properties of XXZ Heisenberg Antiferromagnetic and Ferrimagnetic Nanotubes

  鲜于正楠, 杜安

  理论物理通讯. 2018, 70(06): 823-828.

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  The spin-1/2 antiferromagnetic and spin-(1/2, 1) ferrimagnetic single-walled nanotubes are described by XXZ Heisenberg model. The sublattice magnetization and the critical temperature of the system are calculated by using the double-time spin Green's function method. At zero temperature, with the increase of the exchange interaction in the circumferential direction, a maximum value appears in the sublattice magnetization curves of antiferromagnetic and ferrimagnetic systems. As the diameter of the tube increases, the spin quantum fluctuations and thermal fluctuations are suppressed. In addition, the spin quantum fluctuation of the spin-1/2 antiferromagnetic system is greater than that of the spin-(1/2, 1) ferrimagnetic system. The critical temperature of the system increases firstly and then tends to a constant with the increase of the diameter of tube, and it decreases to zero as the exchange anisotropy of the system disappears.
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  Electron Transport Properties of Graphene-Based Quantum Wires

  赵华, 张小伟, 刘晓春, 郑勇, 刘晚果

  理论物理通讯. 2018, 70(06): 829-833.

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  We study the electronic transport in quantum wire structures made of graphene. By using the nonequilibrium Green function method, the transmission is studied for varies sizes samples. Our results show that the transmission sensitive depends on the size of the system and exhibits fluctuations due to the mismating of propagating modes between the central region and the leads. The number of resonant transmission peaks increases with the increase of length of the wire, while the width of the leads mainly affect the transmission in the region of low energy. A central energy gap in the transmission spectrum is more likely to appear in the quantum wire system than in the uniform armchair graphene nanoribbons. Moreover, the energy gap can be widened for a certain size of the quantum wire system by changing the width of the leads. These results may have potential applications in designing graphene-based devices.