Table of contents

This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He's semi-inverse method (He's variational method). Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.

The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.

Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.

In this work, we study the generalized Rosenau—KdV equation. We shall use the sech-ansätze method to derive the solitary wave solutions of this equation.

Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schrödinger equation of D-dimensional Hulthén potential is transformed to a hyper geometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the "k/2π scale" and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.

In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.

For the time-dependent harmonic oscillator and generalized harmonic oscillator with or without external forces in non-commutative space, wave functions, and geometric phases are derived using the Lewis—Riesenfeld invariant. Coherent states are obtained as the ground state of the forced system. Quantum fluctuations are calculated too. It is seen that geometric phases and quantum fluctuations are greatly affected by the non-commutativity of the space.

We point out a new route to deducing integration formulas, i.e., using the technique of integration within an ordered product (IWOP) of operators we derive some new integration formulas, which seems concise. As a by-product, some new operator identities also appear.

We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum states more effectively.

A new application of cluster states is investigated for quantum information splitting (QIS) of an arbitrary three-qubit state. In our scheme, a four-qubit cluster state and a Bell state are shared by a sender (Alice), a controller (Charlie), and a receiver (Bob). Both the sender and controller only need to perform Bell-state measurements (BSMs), the receiver can reconstruct the arbitrary three-qubit state by performing some appropriately unitary transformations on his qubits after he knows the measured results of both the sender and the controller. This QIS scheme is deterministic.

In this paper, we propose an optical scheme to generate four-mode cluster-type entangled coherent states (ECSs) in free traveling optical fields by using two single-photon sources, coherent state sources, beam splitters, photodetectors, cross-Kerr media, and phase shifters. And the success probability of the states preparation is calculated. At last we discuss the experimental feasibility of such proposal.

This paper investigates the entanglement of a two-qutrit Heisenberg XXX chain with nonlinear couplings under an inhomogeneous magnetic field. By the concept of negativity, we find that the critical temperature increases with the increase of inhomogeneous magnetic field b. Our study indicates that for any |K| > |J|, or |K| < |J| entanglement always exists for certain regions. We also find that at the critical point, the entanglement becomes a nonanalytic function of B and a quantum phase transition occurs.

The quadrupole mode frequency, the monopole mode frequency, and the critical rotational frequency for stirring a single vortex nucleation along the BEC-BCS crossover are obtained. The results show that, in a rotating anisotropic anharmonic trap, the quadrupole mode frequency and the critical rotational frequency for stirring a single vortex nucleation are modified significantly when the system crosses from the BEC side to the BCS side: the anisotropy of the trap induces a downshift of the quadrupole mode frequency and the critical rotational frequency and helps the vortex formation in the system, while an anharmonic trap induces an upshift of the quadrupole mode frequency and the critical rotational frequency and suppresses the vortex formation in the system.

We propose an experimentally feasible scheme to implement the economical 1 → M phase-covariant telecloning based on cavity QED. By the resonant interaction of the atoms with cavity field of a high-Q cavity and the different coupling strength between atoms and cavity field, the scheme can generate quantum entanglement channel in one step. What is more, the operation time and steps do not increase with the increase of atoms.

Far from the horizon of a black hole of even space dimension n, a mass-less field decays as t^1−2l−n in the time, where l is a harmonic mode of the sphere.

We compute the mass and temperature of third order Lovelock black holes with negative Gauss—Bonnet coefficient α₂ < 0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k = −1, the third order Lovelock black holes are thermodynamically stable for the whole range r₊. When k = 1, we found that the black hole has an intermediate unstable phase for D = 7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient is under a critical value. For D ≥ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient is under a critical value for D = 8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon do not depend on the Lovelock coefficients and are the same as those of black holes in general gravity.

In this paper, we use the metric coefficients and the equation of motion obtained in the second post-Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GAIA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-arcsecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.

The logistic growth model with correlated additive and multiplicative Gaussian white noise is used to analyze tumor cell population. The effects of perfectly correlated and anti-correlated noise on the stationary properties of tumor cell population are studied. As in both cases the diffusion coefficient has zero point in real number field, some special features of the system are arisen. It is found that in both cases, the increase of the multiplicative noise intensity cause tumor cell extinction. In the perfectly anti-correlated case, the stationary probability distribution as a function of tumor cell population exhibit two extrema.

Bacterial quorum sensing (QS) has attracted much interests and it is an important process of cell communication. Recently, Bassler et al. studied the phenomena of QS regulated by small RNAs and the experimental data showed that small RNAs played important role in the QS of Vibrio harveyi and it can permit the fine-tuning of gene regulation and maintenance of homeostasis. According to Michaelis—Menten kinetics and mass action law in this paper, we construct a mathematical model to investigate the mechanism induced QS by coexist of small RNA and signal molecular (AI) and show that there are periodic oscillation when the time delay and Hill coefficient exceed a critical value and the periodic oscillation produces the change of concentration and induces QS. These results are fit to the experimental results. In the meanwhile, we also get some theoretical value of Hopf Bifurcation on time deday. In addition, we also find this network is robust against noise.

Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV (GCCKdV) equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonic collisions are presented: (i) two solitons merge and separate from each other periodically; (ii) two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; (iii) two solitons are fluctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the α increasing. Amplitude of v increase with the α increasing and decrease with the β increasing.

We study dynamics in two mutually coupling multi-quantum-well lasers. We carry out theoretical and numerical analysis of synchronization, anti-synchronization, in-phase locking in the two identical lasers but detuning, in detain. It is proved that the coupling level determines stability of the lasers by analyzing the eigenvalue equation. Critical case of locking is discussed via the phase difference equation. Quasi-period and stable states in the two lasers are investigated via varying the current, detuning and coupling level.

In a simple hadronic model, the two-photon exchange contributions to the single spin asymmetries for the nucleon and the ³He are estimated. The results show that the elastic contributions of two-photon exchange to the single spin asymmetries for the nucleon are rather small while those for the ³He are relatively large. Besides the strong angular dependence, the two-photon contributions to the single spin asymmetry for the ³He are very sensitive to the momentum transfer.

The newly synthesized element 117 and its alpha-decay chains are systematically investigated in the framework of the relativistic mean field theory with parameter sets NL-Z2 and TMA. The ground-state properties of the superheavy nuclei on the alpha-decay chains of ²⁹⁴117 and ²⁹³117 are calculated. The experimental alpha-decay energies and half-lives of the two alpha-decay chains are reasonably reproduced by the model. The detailed discussions on the binding energies, alpha-decay energies, half-lives, quadrupole deformations, potential energy curves, and single particle levels of the two alpha-decay chains are made.

We investigate theoretically the single-photon scattering by a Λ-type three-level system interacting with a whispering-gallery-type resonator which is coupled to a one-dimensional waveguide by full quantum-mechanical approach. The single-photon transmission amplitude and reflection amplitude are obtained exactly via real-space approach. The single-photon transport properties controlling by classic optical field are discussed. The critical coupling condition in the coupled waveguide-whispering-gallery resonator-atom with three-level system is also analyzed.

In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation (DFG) signals and sum frequency generation (SFG) signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.

Body-centered tetragonal C4 (bct C4) is a new form of crystalline sp³ carbon, which is found to be transparent, dynamically stable at zero pressure and more stable than graphite beyond 18.6 GPa. Symmetry analysis of the vibrational modes of bct C4 at Brillouin zone center is performed, Raman and infrared active modes are identified. The analysis results show that, different from cubic diamond and hexagonal diamond, there is an infrared active mode in bct C4. Based on first-principle method within the local density approximation, vibrational frequencies, Born effective charge tensors, and infrared absorption intensity of bct C4 are obtained. The vibrational modes of bct C4 are presented and compared with those of cubic diamond and hexagonal diamond in detail.

The adsorption of hydrogen molecule on the external surface of pure C₁₂₀ nanocapsule and endohedrally H₂@C₁₂₀ complex has been examined using the density functional theory calculations. Several different bonding configurations are considered for the hydrogen molecule approaching the outer surface of the considered nanocages. It has been found that the adsorbed H₂ molecule bound weakly to the outer surface of the pure C₁₂₀ nanocapsules in agreement with the recent experimental and theoretical results while, it prefers to be adsorbed rather strongly on the side wall of the endohedrally H₂@C₁₂₀ complex. The adsorption of a single layer and bi-layer of two H₂ molecules on the most stable states of the considered H₂@C₁₂₀ complex appears to be feasible, although the molecules of the second layer are weakly bound. Furthermore, it is found that the formation of 100% coverage is favorable thermodynamically, which corresponds to about 20% by weight storage of H₂ molecules. Thus, surprisingly, we arrive at the prediction that the C₁₂₀ nanocapsules can be implemented as a novel material for energy storage.

We consider the covalence characters of the 3d electron with the e_g orbital freedoms and put forward a new mechanism of the orbital ordering (OO) based on the direct coulomb repulsion in this article. The results show that the orbital-orbital interaction (OO-I) between the adjacent ions in 180-degree configuration is dominated by the super-exchange energy accompanied by a weak orbital-spin coupling, and the OO-I in 90-degree configuration is monitored by the oxygen on-site coulomb repulsion. The ferro-OO is the stable ground state for the one-dimensional chain in the case of the 90-degree configuration.

A complex longitudinal magnetoresistance (MR_//) effect in the non-stoichiometric silver chalcogenides (include the silver selenide and telluride) has been found, however the mechanism for the MR_// effect is not clear now. In this work, a new random resistor network for MR_// effect is proposed based on the experimental observation. The network is constructed from six-terminal resistor units and the mobility of carries within the network has a Gaussian distribution. Considering the non-zero transverse-longitudinal coupling in materials, the resistance matrix of the six-terminal resistor unit is modified. It is found that the material has the "chiral" transverse-longitudinal couplings, which is suggested a main reason for the complex MR_// effect. The model predictions are compared with the experimental results. A three dimension (3D) visualization of current flow within the network demonstrates the "current jets" phenomenon in the thickness of materials clearly.

The relaxation of a one-dimensional magnetic nanoparticle linear chain with lattice constant a is investigated in absence of applied field. There is an equilibrium state (or steady state) where all magnetic moments of particles lie along the chain (x-axis), back to which the magnetic nanoparticle chain at other state will relax. It is found that the relaxation time T_x is determined by T_x = 10^β × a³. This relaxation is compared with that of single magnetic nanoparticle system.