A difference Hamiltonian operator with three arbitrary constants is presented. When the arbitrary constants in the Hamiltonian operator are suitably chosen, a pair of Hamiltonian operators are given. The resulting Hamiltonian pair yields a difference hereditary operator. Using Magri scheme of bi-Hamiltonian formulation, a hierarchy of the generalized Toda lattice equations is constructed. Finally, the discrete zero curvature representation is given for the resulting hierarchy.

Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well.

A new method is used to determine the nonclassical potential symmetry generators of Burgers equation. Some classes of new explicit solutions, which cannot be obtained by Lie symmetry group of Burgers equation or its integrated equation, are obtained by using these new nonclassical potential symmetry generators.

By a known transformation, (2+1)-dimensional Brioer--Kaup equations are turned to a single equation. The classical Lie symmetry analysis and similarity reductions are performed for this single equation. From some of reduction equations, new exact solutions are obtained, which contain previous results, and more exact solutions can be created directly by abundant known solutions of the Burgers equations and the heat equations.

For a relativistic Birkhoffian system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results.

In this paper, four transformations are introduced to solve single sine-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the single sine-Gordon equation.

The correspondence between quantum level spacing distributions and classical motion of 1-D PT symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V₁(x)=(ix)^(2n+1)/m and general polynomial potential V₂(x)= x^2M+ib₁x^2M-1+b₂x^2M-2+ …+ib_2M-1x. The level spacing distribution of V₁ has two forms. When 2n+1-2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n+1-2m is negative. The PT symmetry of this system is spontaneously broken as 2n+1-2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V₂ assumes an increasing power function when order of the polynomial is greater than two.

We have discussed the system which consists of two nonidentical two-level atoms trapped simultaneously in a large-detuned single-mode cavity field in this paper. The results show that it is possible to generate maximally entangled states for two nonidentical two-level atoms only if the cavity frequency and difference of two nonidentical atoms transition frequency are selected and the cavity-atom interacation time is controlled.

We propose a scheme to probabilistically teleport an unknown arbitrary three-level two-particle state by using two partial entangled two-particle states of three-level as the quantum channel. The classical communication cost required in the ideal probabilistic teleportation process is also calculated. This scheme can be directly generalized to teleport an unknown and arbitrary three-level K-particle state by using K partial entangled two-particle states of three-level as the quantum channel.

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional helium in a magnetic field. The results show that the ground and low-excited states of helium in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.

When the motion of a particle is constrained, an excess term exists using hermitian form of Cartesian momentum p_i (i=1,2,3) in usual kinetic energy (1/2μ)∑p_i², and the correct kinetic energy turns out to be (1/2μ)∑(1/f_i)p_if_ip_i, where the f_i are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions f_i is given for a charged rigid planar rotator in the uniform magnetic field.

A scheme for teleporting an arbitrary n-particle entangled state via n pairs of non-maximally entangled states is proposed. The probability of successful teleportation is determined only by the smaller coefficients of the partially entangled pairs. The method is very easy to be realized.

We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross-Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bose-condensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas, we discuss the evolution process of the central and side peaks of the interference pattern.

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.

The dynamics of an ensemble of two-level atoms injected into a single-mode cavity is studied in the exact atom-field interaction situation, in which the counter-rotating terms describing the so-called virtual photon processes neglected in the rotating-wave approximation, are considered. The cavity mode is driven by the injected classical field, and the atom is prepared in a coherent superposition of the two levels. We first derive the generalized Lorenz-Haken equation by using the technique of quantum Langevin equation, and then numerically study the dynamics of this equation. We find that the virtual photon processes have strong effects on the dynamics, which can cause the trajectory in phase space of strange attractor spiral around four focus points, and the trajectory is modulated by virtual photon processes. The chaos region in parameter space is now enlarged. It should be stressed that the strange attractor can exist in optical bistability, and whether the atomic coherences and classical field can inhibit chaos depends on the laser frequency.

In this paper, a systematic and powerful scheme is proposed to address a generalized-type synchronization of a class of continuous-time systems, which includes generalized lag synchronization, generalized anticipated synchronization, and generalized synchronization. The presented scheme is used to investigate the generalized-type synchronization of the 4D hyperchaotic oscillator and the hyperchaotic oscillator with gyrators. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme is more powerful than the scalar signal scheme due to Grassi and Mascolo.

In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple, we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like, period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanh-function method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.

We present three diagonal reflecting matrices for the C_N vertex model with open boundary conditions and exactly solve the model by using the algebraic Bethe ansatz. The eigenvector is constructed and the eigenvalue and the associated Bethe equations are achieved. All the unwanted terms are cancelled out by three kinds of identities.

The moment analysis is applied to perform large scale simulations of the rice-pile model. We find that this model shows different scaling behavior depending on the driving mechanism used. With the noisy driving, the rice-pile model violates the finite-size scaling hypothesis, whereas, with fixed driving, it shows well defined avalanche exponents and displays good finite size scaling behavior for the avalanche size and time duration distributions.

We calculate the transverse Ward--Takahashi relation for the vector vertex in momentum space at one-loop order in four-dimensional Abelian gauge theory. We demonstrate explicitly that the result is exactly the same as that derived by using one-loop vector vertex calculations.

We investigate the lepton flavor violation processes pp→eμX induced by R-parity violating interactions at the Tevatron hadron collider. The theoretical calculation and Monte Carlo simulation demonstrate that with a set of suitable cuts on experimental observables, one might be capable to reduce the standard model physical background to a controllable level so that the signals of R-parity violating interactions could be detected distinctively. Furthermore, clear sneutrino information can be abstracted from the purified event sample where other SUSY scalar quark ``pollution'' is heavily suppressed. We conclude that with a reasonable assumption of 10 fb^-1 integrated luminosity, the experiments at the Tevatron machine would have potential to discover sneutrino in the region of m_{\tilde{ν}}≤400 GeV via lepton flavor violation eμ production channels, or extend the mass scale constraint up to m_{\tilde{ν}}≥ 550 GeV at 95% CL.

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow” approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p²-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on self-energy functions A_f(p²), B_f(p²) and effective mass M_f(p²) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.

The energy loss effect in nuclear matter is another nuclear effect apart from the nuclear effects on the parton distribution as in deep inelastic scattering process. The quark energy loss can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of three kinds of quark energy loss parameterizations given in literature and the nuclear parton distribution extracted only with lepton-nucleus deep inelastic scattering experimental data, measured Drell-Yan production cross sections are analyzed for 800 GeV proton incident on a variety of nuclear targets from FNAL E866. It is shown that our results with considering the energy loss effect are much different from those of the FNAL E866, who analyzes the experimental data with the nuclear parton distribution functions obtained by using the deep inelastic lA collisions and pA nuclear Drell--Yan data. Considering the existence of energy loss effect in Drell-Yan lepton pairs production, we suggest that the extraction of nuclear parton distribution functions should not include Drell-Yan experimental data.

By using a new reaction model for light nuclei, the double-differential cross section of n+¹⁴N reactions at E_n=14.2 MeV has been analyzed. In the case of n+¹⁴N reactions, the reaction mechanism is very complex, there are over one hundred opened partial reaction channels even at incident energy E_n=14.2 MeV. In this paper the opened reaction channels are listed in detail. With LUNF code the model calculation is performed to analyze the double-differential cross sections of total outgoing neutron. The calculated results agree fairly with the experimental data. The results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important. ⁵He emission has been considered, but it is only a small contribution to the double-differential cross section at incident energy E_n=14.2 MeV.

Shell effects in particle emission for two doubly magic nuclei ¹³²Sn and ²⁰⁸Pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shell effects in the emission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.

Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators. The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.

A scheme is presented for generating W states for three or four trapped ions in thermal motion. The scheme works in the regime, where the Rabi frequency of the laser field is on the order of the trap frequency, resulting a fast entanglement speed, which is of importance in view of decoherence.

We discuss and analyze absorption-dispersion response for the probe field in a typical four-level atomic system with vacuum-induced coherence (VIC) arising from the cross coupling pathways associated with a pair of upper excited hyperfine levels. We find that VIC effect can preserve electromagnetically induced transparency (EIT) by using the detailed numerical simulations based on the density-matrix equations and analytical calculations in the dressed-state picture. We also show that the atomic hyperfine structure cannot be a hindrance to obtaining EIT.

We study the moving and interaction of the compact-like pulses in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is related to the nonlinear coupling parameter C_nl and the potential barrier height V₀ of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter C_l, the localization parameter q (the nonlinear coupling parameter C_nl) and the potential barrier height V₀. Numerical experiments demonstrate that appropriate C_l is not detrimental to a stable moving of the compact-like pulse. However, the head on interaction of two compact-like pulses in the lattice system with comparatively small C_l leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate C_l results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish C_l brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities.

Based on an integrate-and-fire mechanism, we investigate the effect of changing the efficacy of the synapse, the transmitting time-delayed, and the relative refractoryperiod on the self-organized criticality in our neural network model.

We study the topological structure of the vortex system in a superfluid film. Explicit expressions for the vortex density and velocity field as functions of the superfluid order parameter are derived. The evolution of vortices is also studied from the topological properties of the superfluid order parameter field.

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R'₃, R'₂, and R'₁ lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R₁ line and R₂ line of YAG:Cr³⁺ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr³⁺ ion in YAG:Cr³⁺ is compressed along the [111] direction. Thus, for YAG:Cr³⁺ and ruby, the splitting of t₂³⁴A₂ (or t₂³²E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R₁ and R₂ lines of YAG:Cr³⁺, the temperature-dependent contributions due to EPI are dominant.

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^N-dimensional matrix is reduced to the polynomial problem of N-dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.

By using the transfer matrix method, within the framework of the dielectric continuum approximation, uniform forms for the interface optical (IO) phonon modes as well as the corresponding electron-IO phonon interaction Hamiltonians in n-layer coupling low-dimensional systems (including the coupling quantum well (CQW), coupling quantum-well wire (CQWW), and coupling quantum dot (CQD)) have been presented. Numerical calculations on the three-layer asymmetrical AlGaAs/GaAs systems are performed, and the analogous characteristics for limited frequencies of IO phonon in the three types of systems (CQW, CQWW, and CQD) when the wave-vector and the quantum number approach zero or infinity are analyzed and specified.

We study a four-electron system in a vertically coupled four-layer quantum dot under a magnetic field by the exact diagonalization of the Hamiltonian matrix. We find that discontinuous ground-state energy transitions are induced by an external magnetic field. We find that dot-dot distance and electron-electron interaction strongly affect the low-lying states of the coupled quantum dots. The inter-dot correlation leads to some sequences of possible disappearances of ground state transitions, which are present for uncoupled dots.

In the present paper, we study the existence of metallic ferromagnetism in a cluster of nanometer scale, which is described by the Hubbard model defined on a complete graph. Therefore, the system is highly frustrated with respect to electron hopping. By solving the model exactly, we show that its ground state is fully spin-polarized at half-filling, even if the Coulomb interaction is finite. This conclusion is in sharp contrast to the well-known result for the Hubbard model on a bipartite lattice. As a result, our exact solution strongly suggests that frustration may play an important role in causing metallic ferromagnetism.

The general Lie point symmetry groups of the Nizhnik-Novikov-Vesselov (NNV) equation and the asymmetric NNV equation are given by a simple direct method with help of their weak Lax pairs.

Using the standard Painlevè analysis and the perturbative method, the Painlevè test for the logarithmic branch is investigated. Nine arbitrary functions are obtained and the Bäcklund transformation of the logarithmic branch is given. Using the new type Bäcklund transformation, many exact solutions are obtained.

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.