Table of contents

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.

Combining Adomian decomposition method (ADM) with Padé approximants, we solve two differential-difference equations (DDEs): the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Padé technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Padé technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.

The present work extends the search of Jacobi elliptic function solutions for the multi-component modified Korteweg-de Vries equations. When the modulum m → 1, those periodic solutions degenerate as the corresponding solitary wave and shock wave ones. Especially, exact solutions for the three-component system are presented in detail and graphically.

In this paper, we propose a new cellular automata model to simulate the railway traffic at station. Based on NaSch model, the proposed station model is composed of the main track and the siding track. Two different schemes for trains passing through station are considered. One is the scheme of "pass by the main track, start and stop by the siding track". The other is the scheme of "two tracks play the same role". We simulate the train movement using the proposed model and analyze the traffic flow at station. The simulation results demonstrate that the proposed cellular automata model can be successfully used for the simulations of railway traffic. Some characteristic behaviors of railway traffic flow can be reproduced. Moreover, the simulation values of the minimum headway are close to the theoretical values. This result demonstrates the dependability and availability of the proposed model.

Based on the concept of adiabatic invariant, the perturbation to Noether–Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in phase space are studied. The definition of the perturbation to Noether–Mei symmetry for the system is presented, and the criterion of the perturbation to Noether–Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.

In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrödinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form Ĥ = (1/2)² + V() [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian Ĥ(, ) and give examples to support it.

In this paper, the nonlinear dispersive Zakharov–Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.

Based on the revised geometric measure of entanglement (RGME) proposed by us [J. Phys. A: Math. Theor. 40 (2007) 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state (GSS) in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement (GME) and relative entropy of entanglement (RE). The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan's topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.

We investigate the entanglement evolution of two qubits that are initially in Werner state under the classical phase noise. We discuss the influence of mixture degree on disentanglement. It is showed that the more mixed the state, the shorter is the time of disentanglement.

The entanglement of the generalized two-mode binomial states in the phase damping channel is studied by making use of the relative entropy of the entanglement. It is shown that the factors of q and p play the crucial roles in control the relative entropy of the entanglement. Furthermore, we propose a scheme of teleporting an unknown state via the generalized two-mode binomial states, and calculate the mean fidelity of the scheme.

We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.

A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N – 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the generalized Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.

We propose a deterministic quantum secure direct communication protocol by using dense coding. The two check photon sequences are used to check the securities of the channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.

We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Cartan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.

Taking the intrinsic decoherence effect into account, the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymetric interaction is investigated in this paper. Concurrence, the measurement of entanglement, is calculated. Compared with the anisotropic in XY plane, the DM interaction is another kind of anisotropic antisymmetric exchange interaction. It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement. The DM interaction only acts on the time evolution of the entanglement when the initial state is |ψ(0)⟩ = cosα|01⟩ + sinα|10⟩ and weakens the degree of entanglement. The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |ψ(0)⟩ = cosα|00⟩ +sinα|11⟩. The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.

A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham–Broer–Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.

Using Monte Carlo method with zero-temperature dynamics, we investigate energy evolution of Ising spin configuration on a square lattice. The energies of some configurations exhibit long duration before those configurations reach the final state — ground state or frozen stripe state. For ground-state dynamical realization, the duration occurs when the energy per spin is 4/L, where L is the lattice size. For stripe-state dynamical realization, the energy is slightly higher than 2/L when the duration appears in the last evolution stage. In addition, it is found that the average energy per spin in final state is approximately 2/3L.

In the paper, we study a linear system driven by O–U noise and give a method which is different from the one stated in Europhys. Lett. 40 (1997) 117. We find the same phenomenon of multiplicative stochastic resonance for the response of the system to the signal as the one found in Europhys. Lett. 40 (1997) 117. The merit of our method is that it prevents the complex formulas when making sum from n = 0 to n → ∞ as in Europhys. Lett. 40 (1997) 117, which leads to the approximate results of the figures.

This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system [Physica A 364 (2006) 103]. On the basis of Lyapunov stability theory, two novel nonlinear controllers are respectively designed to guarantee the global exponential projective synchronization (including complete synchronization and anti-synchronization) and lag synchronization. Finally, numerical simulations are given to show the effectiveness of the main results.

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.

Direct modeling of porous materials under shock is a complex issue. We investigate such a system via the newly developed material-point method. The effects of shock strength and porosity size are the main concerns. For the same porosity, the effects of mean-void-size are checked. It is found that local turbulence mixing and volume dissipation are two important mechanisms for transformation of kinetic energy to heat. When the porosity is very small, the shocked portion may arrive at a dynamical steady state; the voids in the downstream portion reflect back rarefactive waves and result in slight oscillations of mean density and pressure; for the same value of porosity, a larger mean-void-size makes a higher mean temperature. When the porosity becomes large, hydrodynamic quantities vary with time during the whole shock-loading procedure: after the initial stage, the mean density and pressure decrease, but the temperature increases with a higher rate. The distributions of local density, pressure, temperature and particle-velocity are generally non-Gaussian and vary with time. The changing rates depend on the porosity value, mean-void-size and shock strength. The stronger the loaded shock, the stronger the porosity effects. This work provides a supplement to experiments for the very quick procedures and reveals more fundamental mechanisms in energy and momentum transportation.

The color number N_c-dependence of the interplay between quark-antiquark condensates ⟨q⟩ and diquark condensates ⟨qq⟩ in vacuum in two-flavor four-fermion interaction models is researched. The results show that the G_S-H_S (the coupling constant of scalar (q)²-scalar (qq)² channel) phase diagrams will be qualitatively consistent with the case of N_c = 3 as N_c varies in 4D Nambu–Jona–Lasinio model and 2D Gross–Neveu (GN) model. However, in 3D GN model, the behavior of the G_S-H_P (the coupling constant of pseudoscalar (qq)² channel) phase diagram will obviously depend on N_c. The known characteristic that a 3D GN model does not have the coexistence phase of the condensates ⟨q⟩ and ⟨qq⟩ is proven to appear only in the case of N_c ≤ 4. In all the models, the regions occupied by the phases containing the diquark condensates hqqi in corresponding phase diagrams will gradually decrease as N_c grows up and finally go to zero if N_c → ∞, i.e. in this limit only the pure ⟨q⟩ phase could exist.

The unparticle effects on t production at the future photon collider are investigated. Distributions of t invariant mass and that for transverse momentum of top quark with respect to Standard Model and unparticle production are predicted. An odd valley with scalar unparticle contribution appears for some values of d_u, which is due to the big cancellation between the contribution from SM and that from unparticle. This character may be used to study the properties of scalar unparticle. Our investigations also show that scalar unparticle may play a significant role in t production at the photon collider if it exists.

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford's law, which states that the frequency of occurrence of each figure, 1–9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford's logarithmic distribution of β-decay half-lives can be explained in terms of Newcomb's justification of Benford's law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford's law. This indicates that Benford's law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.

The contribution of the two particles Fock states for the production of a heavy quark in proton-pion and photon-pion collisions is studied. It is shown that the effect depends strongly on the produced heavy quark mass, and the choice of the factorization scale.

In this paper, we analytically solve the master equation for Jaynes–Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model. The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation ⟨η|, which can arrange master equations of density operators ρ(t) in quantum statistics as state-vector evolution equations due to the elegant properties of ⟨η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant κ we find that the matrix element of ρ(t) at time t in ⟨η| representation is proportional to that of the initial ρ₀ in the decayed entangled state ⟨ηe^−κt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = ∫(d²η/π)⟨η|ρ⟩D(η), which is different from all the previous known representations.

Under the external AC and DC electric field, the effective response of nonlinear spherical coated composites, which obey the constitutive relation of electric displacement and electric field, is investigated in the dilute limit by using the perturbation method. The local potentials in inclusion and host regions are derived at all harmonics. Moreover, the formulae of the effective linear and nonlinear responses are given in the dilute limit.

A investigation of the properties of the bound states of D⁻ centers confined in a parabolic quantum dot has been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic field strength. Detailed calculations of the binding energies for a number of low-lying states show that for field strength less than B = 2.1 T, the D⁻ center confined in a quantum dot possesses two bound states, for 2.1 ≤ B < 2.4 T, there exist three bound states, etc. Further relevant characteristics of the D⁻ center quantum dots in magnetic fields are provided.

The photoabsorption spectra have been calculated for Si_n and Si_nO (n ≤ 5) clusters using time-dependent density-function theory. Our studies suggest that Si_n–1O clusters are relatively stable than those of corresponding Si_n clusters. Moreover, substantial differences are observed among the absorption spectra of different molecules in the energy region (0 ∼ 8 eV). Comparing two different exchange-correlation potentials, local-density and generalized-gradient approximations, both calculated optical spectra present the same spectral feature.

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line.

We consider a Ginzburg–Landau modified model of layered high-temperature superconductor under pressure. We have theoretically studied the relation between the pressure and the temperature of layered high-temperature superconductor. If the pressure is not a constant, we have a relation of quadratic equation between the pressure and the temperature of layered high-temperature superconductor. In a special case, we find the critical temperature decreases with further increasing pressure. In another special case, the critical temperature increases with further increasing pressure.

We report the oscillating propagation of kink in a nondissipative Frenkel–Kontorova (FK) chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink is transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.