Table of contents

Starting from a special Bäcklund transform and a variable separation approach, a quite general variable separation solution of the generalized (2+1)-dimensional perturbed nonlinear Schrödinger system is obtained. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.

We show that a direct perturbation theory can be used to give a systematic description of the evolution of breather in perturbed sine-Gordon equation. The error in inverse scattering method is also pointed out and corrected to obtain the accurate results.

Making use of the full information obtained in our previous discussions, a new analytical solutions for the potential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzing the similar subjects in porous media.

This article discusses the separability of the pure and mixed states of the quantum network of four nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.

Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained. The exact DDFSSs of the resulting equations are explicitly exhibited.

The Casimir force of the quantized electromagnetic field in the squeezed vacuum state is calculated between a pair of parallel perfectly conducting plates at zero temperature.

By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.

We study the quantum standard teleportation based on the generic measurement bases. It is shown that the quantum standard teleportation does not depend on the explicit expression of the measurement bases. We have given the correspondence relation between the measurement performed by Alice and the unitary transformation performed by Bob. We also prove that the single particle unknown states and the two-particle unknown cat-like states can be exactly transmitted by means of the generic measurement bases and the correspondence unitary transformations.

We investigate tunneling dynamics of atomic group consisting of three atoms in Bose–Einstein condensates with Feshbach resonance. It is shown that the tunneling of the atom group depends not only on the inter-atomic nonlinear interactions and the initial number of atoms in these condensates, but also on the tunneling coupling between the atomic condensate and the three-atomic molecular condensate. It is found that besides oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate atoms on the tunneling dynamics is studied. It is indicated that de-coherence suppresses the atomic group tunneling.

In this paper, we have studied tunneling dynamics of the halves of a double-well trap containing a Bose–Einstein condensate. It is found that there exist step structure and macroscopic quantum self-trapping of population difference of atoms, and exist Shapiro-like steps of atomic tunneling current. Both the population difference and the atomic tunneling current depend strongly on the total number of atoms and the initial phase difference.

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.

With unified colored noise approximation, the steady state distribution function in dispersive optical bistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phase transition is also derived with numerical method. It is found that the number of extremes at non-zero values of the output field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-like phase transition.

We introduce the predictive control into the control of chaotic system and propose a neural network control algorithm based on predictive control. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. The proposed algorithm is simple and its convergence speed is much higher than existing similar algorithms. The control system can control hyperchaos. We analyze the stability of the control system and prove the convergence property of the neural controller. The theoretic derivation and simulations demonstrate the effectiveness of the algorithm.

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localized structures like peakon solution and compacton solution of this new system are found by selecting appropriate functions.

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern–Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern–Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.

In this paper, we recast the matter part of the open superstring star in the present of a constant B field. By using a different coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables. Fortunately we find it does not depend on the value of the B field.

Based on the factorization theorem for lepton induced hard diffractive scattering and color octet heavy quarkonium production mechanism, η_c diffractive production in the direct photon process is studied. The results show that this process can be measured at DESY HERA, and η_c production has different features from J/ψ production, which is weakly affected by the initial and final state gluon radiation. Therefore, η_c photoproduction can be viewed as reliable estimate. The experimental study of this process can give valuable insight in the color octet heavy quarkonium production mechanism.

The sunset diagram of $\lambda\phi^4$ theory is evaluated numerically in cutoff scheme and a nonzero finite term (in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This finding dramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in our previous work.

An effective model used to describe the strange hadronic matter with nucleons, Λ-hyperons, and Ξ-hyperons is extended to finite temperature. The extended model is used to study the density, temperature, and strangeness fraction dependence of the effective masses of baryons in the matter. The thermodynamical quantities, such as free energy and pressure, as well as the equation of state of the matter, are given.

We investigate the properties of $\Lambda_c^+$- and $\Lambda_b$-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no $\Lambda_c^+$ bound states can exist if the $\Lambda_c^+$ potential well depth $|U_{\Lambda_{c}^+}|$ in nuclear matter is less than 10 MeV. If $|U_{\Lambda_{c}^+}|$ is less than 20 MeV, $\Lambda_c^+$ cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the $\Lambda_c^+$-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the $\Lambda_c^+$ in hypernuclei is also observed, and for the $\Lambda_b$ it is nearly zero.

Deformation effects on particle emission in a fission process of ²⁵¹Es nucleus as functions of excitation energy, angular momentum, and viscosity coefficient have been investigated in detail within the framework of Smoluchowski equation. Our calculations show that high excitation energy, low angular momentum, and large viscosity will enhance the influence of deformation on multiplicity of prescission particles, and that the roles of these three parameters will become weak with decreasing deformation.

The interaction of N identical atoms with both a quantized cavity field and an external classical pumping field with the fields being degenerate in frequency, is studied in the regime where the atoms and fields are highly detuned. This dispersive interaction can be used to generate coherent states for the cavity field. By preparing the injected atoms in a superposition of the bare atomic states, various types of Schrödinger-cat-like states may be generated.

We propose a method for generating SU(1,1) intelligent states for the center of mass and relative motional modes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the same as the direction of the two trapped ions' alignment. Under certain conditions, our desired states are obtained as the steady-state solution of the master equation of the system.

We propose a scheme for the generation of superpositions of two Bloch states for a collection of ions. In the scheme the ions are trapped in a linear potential and interact with laser beams. Our scheme does not put any requirement on the Lamb–Dicke parameters.

According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bring forward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granular flow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermal conductivity in the mixed system changes with the fractal parameters such as the solid fraction υ, structural character parameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermal conductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental data and the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generality of our prediction on the granular system.

First-principles LMTO-ASA band calculations are performed for Ga_1-xFe_xAs (x=1, 1/4, 1/8) by assuming supercell structures. It is found that the antiferromagnetic (AFM) state is stable for x=1/4. For x=1/8, ferromagnetic (FM) state is more stable than AFM state, and no stable magnetic state exists for x=1. In both the cases the magnetic moments of As and Ga atoms are parallel to those of the nearest Fe atoms due to the p-d hybridization. Further, the band structure shows rather localized Fe 3d state in the gap, and the parallel polarization is confined rather in the vicinity of Fe site.

The spin-1 Ising model with biaxial crystal-field on the honeycomb lattice is investigated by using the effective-field theory with self-spin correlations and the differential operator technique. The effects of biaxial crystal-field described by two uniaxial anisotropy parameters D_x and D_y on the phase transition and specific heat and susceptibility are studied numerically. Some interesting results are observed in the system such as tricritical behavior depending sensitively on the strength of the biaxial crystal-field.

The equilibrium magnetization configuration, the inducing field and the coercive field in trilayer magnetic materials having an out-of-plane anisotropy defect interlayer between two in-plane anisotropy layers are discussed by both analytical and numerical calculations based on a micromagnet approach. It is shown that the above physical parameters strongly depend on the defect layer such as its thickness and exchange stiffness etc., as well as on the applied fields. It is found that there is a special thickness of defect layer, in which the inducing effect begin to occur, and the critical behavior of inducing field in the vicinity of the special thickness is linearly characterized. Particularly, the magnetic hysteresis shows typical soft hysteresis shape, even though the host material is composed of hard magnets, and the coercivity increases with increasing the thickness of the interlayer.