Table of contents

The new method for constructing the Wronskian entries is applied to the Boussinesq equation. The novel Wronskian solutions to it are obtained, including solitons, rational solutions, Matveev solutions, and complexitons.

Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo–Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.

Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schrödinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.

Under the travelling wave transformation, Calogero–Degasperis–Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero–Degasperis–Focas equation.

A constant-potential system driven by multiplicative dichotomous noise and subject to an input oscillatory signal is investigated. Two phenomena of stochastic resonance are observed. One is the response as a function of the noise's parameters; the other is that as a function of the input signal frequency. A phenomenon of multi-resonance (there are three or four peaks) is found for the response as a function of a parameter of the noise. A phenomenon of reverse-resonance is found, for which the response of the system to the signal can be weakened by the presence of the noise (there is an optimal minimum). These results help in studies of the systems with multiplicative dichotomous noise, such as the semiconductor, the proteins motor, the chemical reaction, and so on.

In this paper, some solutions of a generalized Riccati equation are investigated, which are given in the recent articles [Chaos, Solitons & Fractals 24 (2005) 257; Phys. Lett. A 336 (2005) 463], and the relationship among the solutions is revealed.

In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.

The unified symmetry of a nonholonomic system of non-Chetaev's type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev's type with variable mass in event space at one time. An example is given to illustrate the application of the results.

In this paper, quantum teleportation of one-to-many using (n+1)-particle entanglement is presented. If the sender (Alice) wants to transmit an unknown quantum state to a distant receiver (Bob), similar to the previous schemes, Alice performs Bell-state measurement on particles belonging to herself and informs the receiver the results through the classical channel. After that, it needs to perform the Hadamard operation on the other (n−1) particles and measure them as well. With the aid of the measurement results, Bob can operate a corresponding unitary transformation on his particle to reconstruct the original state. Of course, the reconstruction may realize at either location of n, but it cannot realize at all locations at the same time.

We propose a scheme to produce quantum phase gates for trapped ions. Taking advantage of the adiabatic evolution, the operation is insensitive to small fluctuations of experimental parameters. Furthermore, the spontaneous emission is suppressed since the ions have no probability of being populated in the electronic excited states.

The exact expressions of Gaussian-perturbation matrix elements in one- and two-mode Fock states are derived by virtue of the technique of integration within an ordered product of operators and the entangled state representation. It turns out that the matrix elements are just related to Gegenbauer polynomial and Hypergeometric function respectively. The 1st- and 2nd-order corrections to the energy levels and the 1st-order correction to wavefunctions of harmonic oscillator are deduced.

For the first time we construct the eigenstate |τ⟩ of noncommutative coordinate. It turns out that |τ⟩ is an entangled state in the ordinary space. Remarkably, its Schmidt decomposition has definite expression in the coordinate representation and the momentum representation. The ⟨τ| representation can simplify some calculations for obtaining energy level of two-dimensional oscillator in noncommutative space.

We present a quantum secure communication scheme using three-qubit W state. It is unnecessary for the present scheme to use alternative measurement or Bell basis measurement. Compared with the quantum secure direct communication scheme proposed by Cao et al. [H.J. Cao and H.S. Song, Chin. Phys. Lett. 23 (2006) 290], in our scheme, the detection probability for an eavesdropper's attack increases from 8.3% to 25%. We also show that our scheme is secure for a noise quantum channel.

In this paper, a scheme is proposed for realization of two-qubit controlled-not gates and teleportation of an entangled state of atom-cavity. In this scheme, applying hyperfine levels of atom, we consider Λ-type three-level atom interacting resonantly or nonresonantly with cavity field that is prepared in σ⁻ polarized. We consider the experimental feasibility of this scheme and compare our results with other schemes.

We investigate entanglement transfer from two separate cavities to the excitons in two quantum dots separately placed in the two cavities. The cavity fields and the excitons are treated as two continuous-variable (CV) subsystems. The time-dependent characteristic functions in the Wigner representation for the two subsystems are analytically obtained. Under the conditions that one of the two CV subsystems is initially prepared in a two-mode squeezed vacuum state and the other in its lowest energy state, we show that the entanglement reciprocation between the cavity fields and the excitons is realizable.

A new scheme is proposed for realizing entanglement swapping in cavity QED. The scheme is based on the resonant interaction of two-mode cavity with ∧-type three-level atom, and it involves only a single measurement. In the scheme, the output state after swapping is exactly the maximally entangled state in principle, thus it is prior to the previous one, in which the output state is just approximate. Calculations indicate that our scheme is less influenced by an error.

The free energy at low temperature in 1D sine-Gordon–Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon–Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional generalized Broer–Kaup (GBK) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the (2+1)-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

By means of an improved mapping method and a variable separation method, a series of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.

An integrable (2+1)-dimensional Toda lattice with two discrete variables is investigated again, which is produced from a compatible condition of the Lax triad. The Darboux transformation for its spectral problems is found. As an application, explicit solutions of the (2+1)-dimensional Toda equation with two discrete variables are obtained.

A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian–Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.

In this paper, we show that there exists a twisted duality symmetry between the Maurer–Cartan equations and the equations of motion in the hybrid formalism for the type IIB superstring in an AdS₂×S² background with Ramond–Ramond flux. As a result, from the twisted duality transformation, we construct the Lax connection with the spectral parameter, which ensures the integrability of the system.

Systematic and careful studies are made on the properties of the IJ = 00 ππ and K coupled–channel system, using newly derived dispersion relations between the phase shifts and poles and cuts. The effects of nearby branch point singularities to the determination of the f₀(980) resonance are estimated and discussed.

The structures of Ωω states with spin-parity J^p = 5/2⁻, 3/2⁻, and 1/2⁻ are dynamically studied in both the chiral SU(3) quark model and the extended chiral SU(3) quark model by solving a resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the energies of the baryon ground states, the binding energy of the deuteron, the nucleon-nucleon (NN) scattering phase shifts, and the hyperon-nucleon (YN) cross sections. The calculated results show that the Ωω state has an attractive interaction, and in the extended chiral SU(3) quark model such attraction can make for a Ωω quasi-bound state with spin-parity J^p = 3/2⁻ or 5/2⁻ and the binding energy of about several MeV.

The littlest Higgs model is the most economical one among various little Higgs models. In the context of the littlest Higgs (LH) model, we study the process e⁻γ→ν_eW⁻H and calculate the contributions of the LH model to the cross section of this process. The results show that in most of the parameter spaces preferred by the electroweak precision data, the value of the relative correction is larger than 10%. Such correction to the process e⁻γ→ν_eW⁻H is large enough to be detected via e⁻γ collisions in the future high energy linear e⁺e⁻ collider (ILC) experiment with the c.m. energy (s)^1/2 = 500 GeV and a yearly integrated luminosity £ = 100 fb⁻¹, which will give an ideal way to test the model.

The potential energy surfaces are calculated for neutron-deficient At isotopes from A = 190 to 207 in an axially deformed relativistic mean-field approach, using a quadratic constraint scheme for the first time. We find several minima in the potential energy surface for each nucleus, shape-coexistence, and quadratic deform are discussed.

Using a Langevin equation coupled with a statistical model, we calculate pre-scission giant dipole resonance (GDR) γ-ray multiplicity of nuclei ¹⁹⁴Pb, ²⁰⁰Pb, ²⁰⁶Pb, and ²⁰⁰Os. It is demonstrated that with increasing the isospin asymmetry of these fissioning nuclei the sensitivity of the emitted γ multiplicity to the nuclear viscosity coefficient is decreased significantly. For ²⁰⁰Os nucleus, this γ-ray emission is no longer sensitive to the magnitude of the viscosity coefficient. In addition, the effect of the isospin asymmetry on the γ rays as a probe of nuclear dissipation is reduced with increasing angular momentum. These results suggest that to obtain a more accurate information of the viscosity coefficient by the measurement of pre-scission GDR γ-ray multiplicity it is better to choose those compound systems with small isospin asymmetry and low spin.

The excitation functions of two very similar reaction channels, ⁵⁸Fe+²⁰⁸Pb→²⁶⁵Hs+1n  and⁵⁸Fe+²⁰⁹Bi →²⁶⁶Mt+1n are studied in the framework of the dinuclear system conception. The fusion probabilities are found to be strongly subject to the structure of the driving potential. Usually the fusion probability is hindered by a barrier from the injection channel towards the compound nuclear configuration. The barrier towards the mass symmetrical direction, however, also plays an important role for the fusion probability, because the barrier hinders the quasi-fission, and therefore helps fusion.

The formation mechanism for the body-centred regular octahedral structure of Li₇ cluster is proposed. The curve of the total energy versus the separation R between the nucleus at the centre and nuclei at the apexes for this structure of Li₇ has been calculated by using the method of Gou's modified arrangement channel quantum mechanics (MACQM). The result shows that the curve has a minimal energy of −52.169 73 a.u. at R = 5.06a₀. When R approaches infinity, the total energy of seven lithium atoms has the value of −51.996 21 a.u. So the binding energy of Li₇ with respect to seven lithium atoms is 0.173 52 a.u. Therefore the binding energy per atom for Li₇ is 0.024 79 a.u. or 0.674 eV, which is greater than the binding energy per atom of 0.453 eV for Li₂, the binding energy per atom of 0.494 eV for Li₃ and the binding energy per atom of 0.632 eV for Li₅ calculated previously by us. This means that the Li₇ cluster may be formed stably in a body-centred regular octahedral structure with a greater binding energy.

Some noclassical properties in electromagnetic field are investigated for the interaction of two-modes initially taken in coherent-state representation with the three-level Ξ-type atom, such as squeezing properties and violation of the Cauchy–Schwartz inequality. The enhancement of field squeezing is found by selective atomic measurement. The Cauchy–Schwartz inequality is violated by the application of the classical field followed by detection in excited state.

We investigated the dynamics of the simple spiral waves of the Selkov reaction-diffusion system with the Lattice Boltzmann method. The results of computer simulation lead to the conclusion that the trajectory of the spiral tip is a small circle, the wavelength and the period decay exponentially when the value of parameter b increases; and the relation between the wavelength and the period is λ∝T^1/2, which is qualitatively the same as that obtained by Ou-Yang Qi from Belousov–Zhabotinsky reaction system.

Two-dimensional granular flow in a channel with small exit is studied by molecular dynamics simulations. We firstly define a key area near the exit, which is considered to be the choke area of the system. Then we observe the time variation of the local packing fraction and flow rate in this area for several fixed inflow rate, and find that these quantities change abruptly when the transition from dilute flow state to dense flow state happens. A relationship between the local flow rate and the local packing fraction in the key area is also given. The relationship is a continuous function under the fixed particle number condition, and has the characteristic that the flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at a high value with negative slope. By use of the relationship, the properties of the flow states under the fixed inflow rate condition are discussed in detail, and the discontinuities and the complex time variation behavior observed in the preexisting works are naturally explained by a stochastic process.

Lattice wave of magnetized spherical dust in radio-frequency sheath with negative ions is investigated. The dispersion relation of two-dimensional hexagonal lattice horizontal wave and the influence of negative ions and magnetic field intensity on the wave are also investigated. The results show that for two-dimensional hexagonal horizontal lattice wave, negative ions reduce the wave frequency at the range of long-wavelength, whereas raising the wave frequency at the range of short-wavelength and magnetic field contributes to dropping the wave frequency a little.

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time τ of the Brownian process is greater than the mean collision time τ_c, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state: the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.

With the help of the elastic wave theory, in the perturbed approximation the density-of-states for vibrational modes and the specific heat are studied for different hollow Si nanospheres, coupled with a semi-infinite substrate. We find that the modes of such coupled hollow spheres are significantly broadened and shifted toward low frequencies. The specific heat of the coupled hollow nanosphere is bigger than an isolated one due to the coupling interaction and quantum size effects. The predicted coupling and size enhancements on specific heat are probed in thermal experiments.

To understand the electronic and magnetic properties, we have studied Cr-doped zinc-blende AlN system in detail by applying a first-principle plane wave pseudopotential method based on the density functional theory within the local spin density approximation. The analyses of the band structures, density of states, exchange interactions, and magnetic moments show that Al_1−xCr_xN alloys may exhibit a half-metallic ferromagnetism character, that Cr in the diluted doping limit forms near-midgap deep levels, and that the total magnetization of the cell is 3μ_B per Cr atom, which does not change with Cr concentration. Moreover, we have succeeded in predicting that Al_1−xCr_xN alloys in x = 0.0625 has a very high Curie temperature, and find that ferromagnetic exchange interaction between magnetic dopants is short-ranged.

We study the attack vulnerability of network with duplication-divergence mechanism. Numerical results have shown that the duplication-divergence network with larger retention probability σ is more robust against target attack relatively. Furthermore, duplication-divergence network is broken down more quickly than its counterpart BA network under target attack. Such result is consistent with the fact of WWW and Internet networks under target attack. So duplication-divergence model is a more realistic one for us to investigate the characteristics of the world wide web in future. We also observe that the exponent γ of degree distribution and average degree are important parameters of networks, reflecting the performance of networks under target attack. Our results are helpful to the research on the security of network.

In this paper, we investigate coherence resonance (CR) and noise-induced synchronization in Hindmarsh–Rose (HR) neural network with three different types of topologies: regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.

Based on the Eigen and Crow–Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gaussian distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes (noise of environments) and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.