Table of contents

We firstly propose two kinds of new multi-component BKP (mcBKP) hierarchy based on the eigenfunction symmetry reduction and nonstandard reduction, respectively. The first one contains two types of BKP equation with self-consistent sources whose Lax representations are presented. The two mcBKP hierarchies both admit reductions to the k-constrained BKP hierarchy and to integrable (1+1)-dimensional hierarchy with self-consistent sources, which include two types of SK equation with self-consistent sources and of bi-directional SK equations with self-consistent sources.

In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual-spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state space. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.

For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new intermediate coordinate-momentum representation for a two-particle system is proposed and applied to some two-body dynamic problems.

In this paper, we investigate the evolution of two non-identical two-level atoms in two-mode cavity fields. We demonstrate the death and rebirth effect of entanglement for two non-identical two-level atoms under some initial conditions. It is also exemplified that entangled states of two nonidentical two-level atoms can be generated by entangled two-mode cavity fields. This research can be considered as a first step to further investigate the problem of manipulating two nonidentical two-level atoms in two-mode cavity fields.

A (n, n)-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.

In this paper we propose a tripartite scheme for splitting an arbitrary 2-qubit quantum information by using two asymmetric W states as the quantum channel. In the schemem if the two recipients collaborate together, they can deterministically recover the quantum information by performing first a 4-qubit collective unitary operation and then two single-qubit unitary operations. In addition, since the asymmetric W states are employed as the quantum channel, the scheme is robust against decoherence.

An improvement (Y-protocol) [Commun. Theor. Phys. 49 (2008) 103] on the quantum secure direct communication with W state (C-protocol) [Chin. Phys. Lett. 23 (2006) 290] is proposed by Yuan et al. The quantum bit error rate induced by eavesdropper is 4.17% in C-protocol and 6.25% in Y-protocol. In this paper, another improvement on C-protocol is given. The quantum bit error rate of the eavesdropping will increase to 8.75%, which is 1.1 times larger than that in C-protocol and 0.4 times larger than that in Y-protocol.

A simple scheme for teleporting an unknown M-qubit cat-like state is proposed. The steps of this scheme can be summarized simply: disentangle-teleport-reconstruct entanglement. If proper unitary operations and measurements from senders are given, the teleportation of an unknown M-qubit cat-like state can be converted into single qubit teleportation. In the meantime, the receiver should also carry out right unitary operations with the introduction of appropriate ancillary qubits to confirm the successful teleportation of the demanded entangled state. The present scheme can be generalized to teleport an unknown M-quNit state, i.e., an M-quNit state can be teleported by a single quNit entangled pair.

We present a scheme for probabilistic remote preparation of a tripartite qutrit entangled state with a partial tripartite qutrit entangled state and a partial bipartite qutrit entangled state as the quantum channel. It is found that a bipartite qutrit orthogonal projective measurement, an auxiliary qutrit particle, and the corresponding unitary transformation are required. A scheme for probabilistic remote preparation of a tripartite qudit equatorial entangled state by using a partial tripartite qudit entangled state and a partial bipartite qudit entangled state as the quantum channel is also proposed. We calculate the successful total probability and the total classical communication cost required in the RSP process, respectively.

In this letter, we propose a scheme of a special quantum optical Fredkin gate assisted by optical manipulations and postselection from the coincidence measurements, and then modify it with cross-Kerr nonlinearities to be suitable for the realization of all possible positive operator-valued measurements of bipartite polarization states. This scheme is feasible in the lab with the current experimental technology.

We propose a scheme for realization a quantum Controlled-NOT gate operation using two four-level atoms through a selective atom–cavity interaction in cavity quantum electrodynamics system. In our protocol, the quantum information is encoded on the stable ground states of the two atoms. During the interaction between atoms and single-mode vacuum cavity-field, the atomic spontaneous emission is negligible as the large atom–cavity detuning effectively suppresses the spontaneous decay of the atoms. The influences of the dissipation and the deviation of interaction time on fidelity and corresponding success probability of the quantum Controlled-NOT gate and the experimental feasibility of our proposal are also discussed.

In the present work, a simple scheme for the direct measurement of the concurrence of two-qubit pure states is proposed. The scheme is based on trapped ions and only needs one step when the two identical pure states are given. The vibrational mode in our proposal is only virtually excited, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.

We consider the one-dimensional nonlinear Schrödinger equations that describe the dynamics of a Bose–Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrödinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential. We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.

By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension d_f, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time τ_c, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τ_B to the steady state becomes shorter with increasing values of d_f. In the steady state, the spatial density distribution becomes more clusterized as d_f increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of d_f. Also, the density clusterization is explained from the correlations.

In the paper, we investigate a globally coupled linear system with finite subunits subject to temporal periodic force and with multiplicative dichotomous noise. It is shown that, the global coupling among the subunits can hugely enhance the phenomenon of SR for the amplitude of the average mean field as the functions of the transition rate of the noise and that as the function of the frequency of the signal respectively.

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

This paper analyzes spatial grey self-similar solitary waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. New exact self-similar solutions are found using a novel transformation and their main features are investigated by using direct computer simulations.

The phenomenon of stochastic resonance (SR) in an asymmetric mono-stable system subject to two external periodic forces and multiplicative and additive noise is investigated. It is shown that the signal-to-noise ratio (SNR) for the fundamental and higher harmonics is a non-monotonic function of the intensities of the multiplicative and additive noise, as well as of the system parameter. Moreover, the SNR for the fundamental harmonic decreases with the increase of the system asymmetry, while the SNR for the higher harmonics behaves non-monotonically as the system asymmetry varies.

The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation (MF). The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density ρ^* = ρσ³ = 0.224 and the reduced temperature T^* = kT/∊ = 1.87 (σ is the diameter of Heisenberg hard sphere and ∊ is the coupling constant).

In this paper, by making use of Duan's topological current theory, the branch process of regular magnetic monopoles is discussed in detail. Regular magnetic monopoles are found generating or annihilating at the limit point and encountering, splitting, or merging at the bifurcation point and the degenerate point systematically of the vector order parameter field (x). Furthermore, it is also shown that when regular magnetic monopoles split or merge at the degenerate point of field function , the total topological charges of the regular magnetic monopoles are still unchanged.

In the SU(3) simple group model, the new neutral gauge boson Z' couples to pairs of SM fermions with couplings fixed in terms of the SM gauge couplings and depending only on the choice of the fermion embedding. In this paper, we calculate the contributions of this new particle to the processes e⁺e⁻ → l⁺l⁻, b, and c and study the possibility of detecting this new particle via these processes in the future high-energy linear e⁺e⁻ collider (LC) experiments with √s = 500 GeV and £_int = 340 fb⁻¹. We find that the new gauge boson Z' is most sensitive to the process e⁺e⁻ → b. As long as M_Z' ⩽ 2 TeV, the absolute values of the relative correction parameter are larger than 5%. We calculate the forward-backward asymmetries and left-right asymmetries for the process e⁺e⁻ → c, with both the universal and anomaly-free fermion embeddings. Bounds on Z' masses are also estimated within 95% confidence level.

Rare decay processes K⁺ → π⁺ ν and K_L → π⁰ν are considered in the framework of three-site Higgsless model. The contributions of this new physics model to these two decay processes come from the new heavy gauge bosons and the correction terms for the couplings of the ordinary gauge bosons with fermions. Our numerical results show that the branching ratios of these two decay processes can be enhanced by 40% and 50% relative to those predicted by the standard model.

Using closed orbit theory, we give a clear physical picture description of the Rydberg hydrogen atom near a metal surface and calculate the Fourier transformed recurrence spectra of this system at different scaled energies below ionization threshold. The results show that with the increase of the scaled energy, the number of the closed orbit increases greatly. Some of the orbits are created by the bifurcation of the perpendicular orbit. This case is quite similar to the Rydberg atom in an electric field. When the scaled energy increases furthermore, chaotic orbits appear. This study provides a different perspective on the dynamical behavior of the Rydberg atom near a metal surface.

By using the derivative method, we obtained the same result with that of the previous work of Chen et al. in 2006. Different from the integral form, the derivative form of the surface expression published in this paper is derived from differential equation and based on the theory of non-imaging focusing heliostat proposed by Chen et al. in 2001. The comparison of the derivative form of fixed aberration correction surface has been made with that of integral form surface as well as that of spherical surface in concentrating the solar ray.

We recommend a new convenient method for disentangling some exponential operators and derive a set of new operator identities. Especially, we derive the normal odering form of exp [fa^†a + ga^†2 + ka²] without appealing to Lie algebra method. Application of these formulas in solving some dynamic Hamiltonian is presented.

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Gaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.

The Chinese traditional medical massage has been used as a natural therapy to eliminate some diseases. Here, the effect of the rolling massage frequency to the blood flow in the blood vessels under the rolling massage manipulation is studied by the lattice Boltzmann simulation. The simulation results show that when the frequency is smaller than or comparable to the pulsatile frequency of the blood flow, the effect on the blood flux by the rolling massage is small. On the contrast, if the frequency is twice or more times of the pulsatile frequency of the blood flow, the blood flux is greatly enhanced and increases linearly with respect to the frequency. Similar behavior has also been observed on the shear stress on the blood vessel walls. The result is helpful for understanding that the rolling massage has the function of promoting the blood circulation and removing the blood stasis.

Based on the ϕ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term · (∂_i × ∂_j), and both these topological structures are characterized by the ϕ-mapping topological numbers–Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invariant is a proper topological invariant to describe the knotted solitons.

We investigate theoretically the spin current in a quantum wire with weak Dresselhaus spin-orbit coupling connected to two normal conductors. Both the quantum wire and conductors are described by a hard-wall confining potential. Using the electron wave-functions in the quantum wire and a new definition of spin current, we have calculated the elements of linear spin current density j_s,xi^T and j_s,yi^T (i = x, y, z). We find that the elements j^T_s,xx and j^T_s,yy have a antisymmetrical relation and the element j^T_s,yz has the same amount level as j_s,xx^T and j_s,yy^T. We also find a net linear spin current density, which has peaks at the center of quantum wire. The net linear spin current can induce a linear electric field, which may imply a way of spin current detection.

In this paper, we investigate the decoherence time of a double quantum dot (DQD) charge qubit in three kinds of baths through solving dynamics of the qubit. The dynamics of the qubit is investigated with Redfield master equation. It is shown that the decoherence time of the qubit in Ohmic bath has the same order of magnitude as the experiments reported. When the environment is modeled with the supra-Ohmic bath the decoherence time of the qubit is shorter than the experimental result. And when modeled with the sub-Ohmic bath the decoherence time of the qubit is longer than the experimental result.

Spin-wave theory is used to study magnetic properties of ferromagnetic double layers with a ferrimagnetic interlayer coupling at zero temperature. The spin-wave spectra and four sublattices magnetizations and internal energy are calculated by employing retarded Green function technique. The sublattice magnetizations at ground state are smaller than their classical values, owing to the zero-point quantum fluctuations of the spins.

In this paper we study a negatively charged exciton (NCE), which is trapped by a two-dimensional (2D) parabolic potential. By using matrix diagonalization techniques, the correlation energies of the low-lying states with L = 0, 1, and 2 are calculated as a function of confinement strength. We find that the size effects of different states are different. This phenomenon can be explained as a hidden symmetry, which is originated purely from symmetry. Based on symmetry, the features of the low-lying states are discussed in the influence of the 2D parabolic potential well. It is found that the confinement may cause accidental degeneracies between levels with different low-excited states. It is shown that the effect of quantum confinement on the binding energy of the heavy hole is stronger than that of a light hole.

A systematic analysis of Shanghai and Japan stock indices for the period of Jan. 1984 to Dec. 2005 is performed. After stationarity is verified by ADF (Augmented Dickey–Fuller) test, the power spectrum of the data exhibits a power law decay as a whole characterized by 1/f^β processes with possible long range correlations. Subsequently, by using the method of detrended fluctuation analysis (DFA) of the general volatility in the stock markets, we find that the long-range correlations are occurred among the return series and the crossover phenomena exhibit in the results obviously. Further, Shanghai stock market shows long-range correlations in short time scale and shows short-range correlations in long time scale. Whereas, for Japan stock market, the data behaves oppositely absolutely. Last, we compare the varying of scale exponent in large volatility between two stock markets. All results obtained may indicate the possibility of characteristic of multifractal scaling behavior of the financial markets.

In this paper, the prediction of the track for No. 1 tropical cyclone, Neoguri, is concretely provided by using a special solution to (2 + 1)-dimensional Euler Equation.

Some cylindrically symmetric inhomogeneous viscous fluid string cosmological models with magnetic field and cosmological term Λ varying with time are investigated. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ₁¹ of the shear tensor σ_jⁱ. The value of cosmological constant for the model is found to be small and positive, which is supported by the results from recent supernovae Ia observations. The effect of bulk viscosity is to produce a change in perfect fluid and hence exhibits essential influence on the character of the solution. The physical and geometric properties of the models are also discussed in presence and absence of magnetic field.

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity: one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.

In this paper, we evaluate the general solutions for plane-symmetric thick domain walls in Lyra geometry in presence of bulk viscous fluid. Expressions for the energy density and pressure of domain walls are derived in both cases of uniform and time varying displacement field β. Some physical consequences of the models are also given. Finally, the geodesic equations and acceleration of the test particle are discussed.