Table of contents

Based on the concept of adiabatic invariant, the perturbation to Lie–Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie–Mei symmetry for the system is presented, and the criterion of the perturbation to Lie–Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.

Mei symmetry and Mei conserved quantity for a non-holonomic system of non-Chetaev's type with unilateral constraints in the Nielsen style are studied. The differential equations of motion for the system above are established. The definition and the criteria of Mei symmetry, conditions, and expressions of Mei conserved quantity deduced directly from the Mei symmetry are given. An example is given to illustrate the application of the results.

Considering full perturbation to infinitesimal generators in the Mei structure equation, a new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.

The extended Riccati mapping approach^[1] is further improved by generalized Riccati equation, and combine it with variable separation method, abundant new exact complex solutions for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on a derived periodic solitary wave solution and a rational solution, we study a type of phenomenon of complex wave.

In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution.

For two particles with different spins, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and spin-1/2; spin-1/2 and spin-3/2. We show that for these states Bell's inequality is violated.

We propose two schemes for quantum dense coding without Bell states measurement. One is deterministic, the other is probabilistic. In the deterministic scheme, the initial entangled state will be not destructed. In the probabilistic scheme, the initial unknown nonmaximal entangled state will be transformed into a maximal entangled one. Our schemes require two auxiliary particles and perform single-qubit measurements on them. Thus our schemes are simple and economic.

By exposing deficiency of the usual superoperators that have no explicit operator-expression in quantum information theory we introduce thermo entangled state representation to endow each of these superoperators a definite operator-expression in an enlarged space in which one mode is a fictitious. This helps us to directly derive the role of exponential of superoperators and the solutions of some master equations.

In a previous work [Commun. Theor. Phys. 45 (2006) 79] a scheme was presented for approximate and conditional teleportation of an unknown atomic state in a QED-cavity without Bell-state measurement via two-photon Jaynes–Cummings model in the effective Hamiltonian approach. This comment presents an alternative method, based on the so called 'full two-photon Jaynes–Cummings Hamiltonian approach'. Accordingly, it describes the evolution of the two-photon degenerate process for arbitrary average photon number inside the cavity, as the correct way to implement teleportation in this scenario.

The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel is studied by adopting the entanglement of formation determined by the concurrence. Then, we consider the teleportation by using joint measurements of the photon-number sum and phase difference with the pair cat states as an entangle resource and discuss the influence of amplitude decoherence on the mean fidelity of the teleportation.

We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate (QCPG) operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.

Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditional symmetries (GCSs) is implemented. The reducibility of the initial-value problem for an evolution equation to a Cauchy problem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry. Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.

A quantum secure direct communication scheme using dense coding is proposed. At first, the sender (Alice) prepares four-particle genuine entangled states and shares them with the receiver (Bob) by sending two particles in each entangled state to him. Secondly, Alice encodes secret information by performing the unitary transformations on her particles and transmits them to Bob. Finally, Bob performs the joint measurements on his particles to decode the secret information. The two-step security test guarantees the security of communication.

We analyze the dynamics of a bright soliton in Bose–Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross–Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomic scattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity.

We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross–Pitaevskii equation with the Kronig–Penney potential (KPP) of period d, which governs a repulsive Bose–Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {R_n} corresponding to different chemical potentials {μ_n} from the known solutions of the system. The n-th eigenstate R_n is the Jacobian elliptic function with period 2d/n for n = 1,2,..., and with zero points containing the potential barrier positions. So R_n is differentiable at any spatial point and R_n² describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a δ potential at site x_i to manipulate the transitions from the states of {R_n} with zero point x ≠ x_i to the states of {R_n} with zero point x = x_i. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

We give a study on the general Møller transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of the geodesic equations of motion, the differential form of the general Møller transformation at arbitrary direction is presented.

The possibility of stable or quasi-stable Planck mass black hole remnants as solution to the black hole information paradox is commonly believed phenomenologically unacceptable. Since we need a black hole remnant for every possible initial state, the number of remnants is expected to be infinite and that would lead to remnant pair production in any physical process with a total available energy roughly exceeding the Planck mass. In this note I point out that a positive cosmological constant of the Universe would naturally lead to an upper bound on the number of possible remnants.

Effects of coupling distance on synchronization and coherence of chaotic neurons in complex networks are numerically investigated. We find that it is not beneficial to neurons synchronization if confining the coupling distance of random edges to a limit d_max, but help to improve their coherence. Moreover, there is an optimal value of d_max at which the coherence is maximum.

After presenting the infinite operator-sum form solution to the Milburn equation dρ/dt = γ(UρU^† – ρ) = γU[ρ,U^†], where U = e^-iH/ℏγ, and verifying that this equation preserves the three necessary conditions of density operators during time evolution, we prove that the von Neumann entropy increases with time. We also point out that if A and B both obey the Milburn equation, then the product AB obeys (d/dt) (AB) = γU[AB, U†] – (1/γ) (dA/dt) (dB/dt), which violates the Milburn equation, this reflects that a pure state will evolve to a mixture in general.

In this paper, by applying the extended Jacobi elliptic function expansion method, the envelope periodic solutions and corresponding dark soliton solution, bright soliton solution to Bose–Einstein condensation in linear magnetic field and time-dependent laser field are obtained.

In this article, we assume that the (0⁺, 1⁺) strange-bottom mesons are the conventional b mesons, and calculate the electromagnetic coupling constants d, g₁, g₂, and g₃ using the light-cone QCD sum rules. Then we study the radiative decays B_s0 → B^*_s γ, B_s1 → B_s γ, B_s1 → B^*_sγ, and B_s1 → B_s0 γ, and observe that the widths are rather narrow. We can search for the (0⁺, 1⁺) strange-bottom mesons in the invariant B_s0π⁰ and B^*_sπ⁰ mass distributions in the strong decays or in the invariant B^*_sγ and B_sγ mass distributions in the radiative decays.

B⁰(B_s) → γν decays are useful to determining the decay constants f_B(f_Bs) and B(B_s) meson wave function. Using the B meson wave function determined in hadronic B(B_s) decays, we study the uncertainties due to the types of B meson wave functions. We find that the branching ratios are sensitive to the type of wave functions and input parameters, but the energy spectrum is independent. The predicted branching ratios are (0.45–1.04) × 10^-9 and (2.14–3.27) × 10^-8 for B⁰ and B_s decay, respectively.

In this paper, we discuss the unitary transformation induced by Z₆ rotations of noncommutative space on the states |k,q,⟩, which plays a key role in construction for noncommutative solitons T²/Z₆ by GHS method. As a result, we prove a well-known 'Gauss Sum' formula in the number theory through a concise way.

Based on the generalized vector meson dominance model in QCD, we study photoproduction of vector meson γ off the proton by use of the QCD inspired model in which the contributions from quark-quark, gluon-gluon, and quark-gluon interference term to observable are taken into consideration. Calculations are performed for total cross section σ_tot, differential cross section dσ/dt, ratio of the real part to imaginary part of forward scattering amplitude ρ, and nuclear slop parameter function β. The mediators of interactions between projectiles (the quark and antiquark pair fluctuated from the real the photon) and the proton target (three-quark system) are the tensor Glueball and Odderon instead of using the usual Pomeron exchange. The theoretical predictions for σ_tot (s) are consistent with the experimental data within error bars of the data. The data for dσ/dt, ρ, and β are urgently needed.

We extend our Padé-aided analysis of the nonperturbative renormalization of nucleon-nucleon scattering to the case of coupled channels.

We study the quark loop effects on the dressed gluon propagator and also on the quark propagator itself. We find that the gluon propagators are different in two phases. The quark mass effects on the gluon propagator are small but not negligible. We also study the current quark mass dependence on the bag constant.

Employing the accurate frozen-core full-potential projector augmented-wave method, the self-consistent electronic structure calculations were carried out on pure Ni, Pd, Pt and mixed Ni-Pd and Ni-Pt free-standing linear and zigzag nanowires. The bond lengths for all these systems are generally increased as their structures change from the linear to the zigzag chain. The bond lengths for Ni-Pd and Ni-Pt wires are in between the values of corresponding pure system and the bond angles around 60° suggesting the possible formation of Ni-Pd and Ni-Pt bimetallic materials. In mixed Ni-Pd and Ni-Pt chains, the Ni, Pd, and Pt atoms have quite high local magnetic moments. The calculations suggest that the magnetic moments in linear nanowires are generally larger than the ones of corresponding zigzag nanowires. It is found that there is hybridization between Ni 3d and Pd 4d, Ni 3d and Pt 5d states, which may significantly affect structural stability and magnetism of Ni-Pd and Ni-Pt nanowires.

Recently, inwardly propagating waves (called antiwaves, AWs) in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves (normal waves, NWs) and the other AWs. In this paper we find that negative refraction (NR) in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes (both positive and negative refractions) nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.

Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.

The temporal and spatial dynamics of one weak probe laser pulse, propagating through a A-type atomic medium with two-folded levels under the resonant excitation of one microwave driving field and one strong control field, is investigated in this paper. By numerically solving coupled Bloch-Maxwell equations, it is found that, in the absence of the microwave driving field, the atomic medium is transparent to the probe pulse at line center, which propagates over sufficiently long distances. By contrast, when the microwave driving field is applied, the probe pulse at line center can be rapidly absorbed on propagation. This substantial reduction of probe transmittance caused by the microwave driving field may lead to potential applications in designing a new kind of optical switching.

A single-mode laser noise model driven by quadratic colored pump noise and biased amplitude modulation signal is proposed. The analytic expression of signal-to-noise ratio is calculated by using a new linearized procedure. It is found that there are three different typies of stochastic resonance in the model: the conventional form of stochastic resonance, the stochastic resonance in the broad sense, and the bona fide SR.

In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The 'Sagdeev potential' from the MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, and its amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.

An investigation of the optical properties of a hydrogenic donor in spherical parabolic quantum dots has been performed by using the matrix diagonalization method. The optical absorption coefficient between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wave functions. The results are presented as a function of the incident photon energy for the different values of the confinement strength. These results show the effects of the quantum size and the impurity on the optical absorption coefficient of a donor impurity quantum dot.

We investigate theoretically the spin accumulation in a Rashba spin-orbit coupling (SOC) nanoribbon nonadiabatically connected to a normal conductor. Both the nanoribbon and conductor are described by a hard-wall confining potential. Using the scattering matrix approach within the effective free-electron approximation, we have calculated the out-of-plane spin accumulation in the nanoribbon. It is found that the spin accumulation shifts toward the two edges of nanoribbon with the increasing of propagation modes. Specifically, as the Rashba SOC strength increases the spin accumulation in the nanoribbon will be enhanced and this result may suggest us a simple method to control the spin accumulation of the system by Rashba SOC strength.

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian H_i of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomena occur when the value of the transverse field is not zero and the reentrant diagram is given.

Based on the model of the two calcium stores developed by Goldbeter, the influence of external magnetic field on the calcium concentration has been discussed. We believe that the cell membrane is a major site of interaction for extremely-low-frequency (ELF) electromagnetic fields, and the permeability of ions can be changed with the changing electromagnetic fields. It is shown that magnetic field initiates intracellular calcium oscillation with a threshold in flux density, and that the calcium oscillations do not occur if the density of magnetic field is below the threshold. The results of theoretical calculation are consistent with that of the experiment. The intracellular free calcium concentrations of different cells exposed to the same magnetic fields are different from each other. It is indicated that the different behaviors such as oscillation, rise and invariability of calcium concentration are associated with the sort of cells.

Using a Barkley model as an example, we study spiral waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral breakup.

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.

Nonlinear Rossby waves in a Boussinesq fluid model which includes both the vertical and horizontal components of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wave solution. Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and identify the Rossby cnoidal and solitary waves. Qualitative analysis indicates that if the disturbances are independent of latitude, the effect of horizontal components of Coriolis force disappears.

We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brickwall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking's area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L³ as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.