In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.

A new pseudospectral method was introduced to calculate wavefunctions and energy levels of hydrogen atom in arbitrary potential. Some results of hydrogen atom in uniform magnetic fields were presented, high accuracy of results was obtained with simple calculations, and our calculations show very fast convergence. It suggests a new method for calculations of hydrogen atom in external fields.

Based on the bifurcation and the idea that the solitary waves and shock waves of partial differential equations correspond respectively to the homoclinic and heteroclinic trajectories of nonlinear ordinary differential equations satisfied by the travelling waves, different conditions for the existence of solitary waves of a perturbed sine-Gordon equation are obtained. All of the corresponding approximate solitary wave solutions are given by integrating the derived approximate equations directly.

The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m,n) equations), (u_z^m)_zzτ+γ(u_zⁿu_τ)_z+u_ττ=0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation u_zzzτ+γ(u_zu_zτ+u_zzu_τ)+u_ττ=0, is presented. Five types of symmetries of the E(m,n) equation are obtained by making use of the direct reduction method. Using these obtained reductions and some simple transformations, we obtain the solitary-like wave solutions of E(1,n) equation. In addition, we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they reemerge with the same coherent shape) of E(3,2) equation and E(m,m-1) for its potentials, say, u_z, and compacton-like solutions of E(m,m-1) equations, respectively. Whether there exist compacton-like solutions of the other E(m,n) equation with m≠n+1 is still an open problem.

By virtue of the technique of integration within an ordered product of operators and the Schmidt decomposition of the entangled state |η〉, we reduce the general projection calculation in the theory of quantum teleportation to a as simple as possible form and present a general formalism for teleportating quantum states of continuous variable.

We have studied quantum statistical properties in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation between the two condensates can be nonclassical, which means that there exists a violation of Cauchy-Schwartz inequality. The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.

By making use of the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-de Sitter black hole and obtain the integral expression of black hole's entropy and the entropy to which the cosmic horizon surface corresponds. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, i.e. the membrane model, we calculate black hole's entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon, the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, the physical idea is clear and the calculation is simple. We offer a new simple and direct way for calculating the entropy of different complicated black holes.

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal λφ³ theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.

Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.

We propose a rational quantum deformed nonlocal currents in the homogeneous space SU(2)_k/U(1), and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k=c is obtained. In the classical limit ħ→0, the quantum nonlocal currents become SU(2)_k parafermion, and the realization of Yangian double becomes the parafermion realization of SU(2)_k current algebra.

By solving rigorously the relativistic wave equations derived from Bargmann-Wigner equation for arbitrary spin, the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.

Mixed symmetry states are studied in the framework of the neutron-proton interacting boson model. It is found that some of the mixed symmetry states with moderate high spins change very fast with respect to the Majorana interaction. Under certain conditions, they become the yrast state or yrare state. These states are difficult to decay and become very stable. This study suggests that a possible new mode of isomers may exist due to the special nature in their proton and neutron degrees of freedom.

Total and differential cross sections for K⁺-⁶Li elastic scattering are calculated using the folding optical potential model, in which the influence of three factors is considered including the recoil of target nucleus, the loosely bounded nuclear density and the unusual spin of ⁶Li ground state. The theoretical results are found in pretty good accordance with the existing experimental data at P_K=715 MeV/c.

A method is presented for generating highly squeezed states of a cavity field via the atom-cavity field interaction of the Raman type. In the scheme a sequence of three-level Λ-type atoms interacts with a cavity field, displaced by a classical source, in a Raman manner. Then the atomic states are measured. By this way the cavity field may collapse onto a superposition of several coherent states, which exhibits strong squeezing. The scheme can also be used to prepare superpositions of many two-mode coherent states for two cavity fields. The coherent states in each mode are on a straight line. This is the first way for preparing multi-component entangled coherent states of this type in cavity QED.

A new model — model of random porous media degradation via several fluid displacing, freezing, and thawing cycles is introduced and investigated in this paper. The fluid transport is based on the deterministic method with dispersion effect. The result shows that the topology and the geometry of the porous media have a strong effect on displacement processes. The cluster size of viscous fingering (VF) pattern in percolation cluster increases with the increase of iteration parameter n. When iteration parameter n≥10, VF pattern does not change with n. We find that the displacement fluid forms trapping regions in random porous media with dispersion effect. And the trapping regions will expand with the increasing of the iteration parameter n. When r (throat size) →1 and n≥5, the peak value of the distribution N_mat(r) increases as n increases, where N_mat(r) is the normalized distribution of throat sizes after different displacement-damages but before freezing. The peak value of the distribution N_inv(r) reaches a maximum when n≥10 and r=1, where N_inv(r) is the normalized distribution of the size of invaded throat. This result is different from invasion percolation. It is found that the sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L, and E has a minimum as L increases to the maximum size of lattice. The VF pattern in percolation cluster has one frozen zone and one active zone.

We propose a new method to obtain the correlation length of gapped XXZ spin 1/2 antiferromagnetic chains. Following the relativistic quantum field theory in (1+1) space-time dimensions, we use the exact dispersion of massive spinon to calculate the correlation length for XXZ spin 1/2 chain. We conjecture that the correlation length for other 1D lattice models can be obtained in the same way. Relation between dispersion and the oscillated correlation of gapped incommensurate lattice models is also discussed.

The influence of the electron-phonon coupling on the energy of low-lying states of the barrier D^- center, which consists of a positive ion located on the z-axis at a distance from the two-dimensional quantum dot plane and two electrons in the dot plane bound by the ion, is investigated at arbitrary strength of magnetic field by making use of the method of few-body physics. Discontinuous ground-state energy transitions induced by the magnetic field are reported. The dependence of the binding energy of the D^- ground state on the quantum dot radius is obtained. A considerable enhancement of the binding is found for the D^- ground state, which results from the confinement of electrons and electron-phonon coupling.

In order to understand the properties of the spin system with orbital degeneracy, we first study the ground state of the SU(4) spin-orbital model on a square lattice. The mean-field results suggest that for a small Hund's interaction, the flavor liquid state is stable against the solid state, but with sufficient deviation from the SU(4) limit the long-range order may be attained in 2D system. Furthermore, we employ a variational approach to calculate the phase diagram of the ground state and the temperature-dependent susceptibility by taking into account the Hund's interaction and the anisotropy in orbital wavefunctions. Finally, the implications for the experimental observations on the material, LiNiO₂, are discussed.

By making use of the diagonalization of the complete d³ energy matrix in a trigonally distorted cubic-field and the theory of pressure-induced shifts (PS) of energy spectra, the whole energy spectrum of α-Al₂O₃:Mn⁴⁺ and PS of levels have been calculated. All the calculated results are in excellent agreement with the experimental data. The comparison between the results of α-Al₂O₃:Mn⁴⁺ and ruby has been made. It is found that on one hand, R₁-line and R₂-line PS of α-Al₂O₃:Mn⁴⁺ and ruby are linear in pressure over 0～100 kbar, and their values of the principal parameter for PS are very close to each other. On the other hand, the sensitivities of R₁-line and R₂-line PS of α-Al₂O₃:Mn⁴⁺ are higher than those of ruby respectively, which comes mainly from the difference between the values of parameters at normal pressure of two crystals; moreover, the expansion of d-electron wavefunctions of α-Al₂O₃:Mn⁴⁺ with compression is slightly larger than the one of ruby, and the effective charge experienced by d-electrons of α-Al₂O₃:Mn⁴⁺ decreases with compression more rapidly than the one of ruby. In the final analysis, all these can be explained in terms of the facts that the two crystals are doped α-Al₂O₃ with two isoelectronic ions; the strengths of the crystal field and covalency of α-Al₂O₃:Mn⁴⁺ are larger than those of ruby respectively, due to the charge of Mn⁴⁺ to be larger than that of Cr³⁺.

The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are suitably shaped curves with their upper parts inclined backward properly. The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters, Ra, Pr and Sc. It is shown that the stronger the convection relative to the diffusion in solution is, the more backward the upper parts of the stable crystal growth face and dissolution face are inclined. The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.

Based on the stochastic inclined rods model proposed by H. Matsuura et al., we study the motion of actin myosin system in an overdamped regime. Our model is composed of an inclined spring (rod), a myosin head and a myosin filament. The results of calculation show that the model can convert the random motion to one-directional motion, and the myosin head works as a resonator of random noise, which absorbs the energy through a stochastic resonance. The results show that the inclined rod and the intermolecular potential are very important for the system to move.

In this second paper of a series of papers, we explore the difference discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multi-parameter differential approach. In terms of the difference discrete Euler-Lagrange cohomological concepts, we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler-Lagrange or canonical equations derived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrange cohomological conditions are satisfied.

The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model. To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters. In this paper, we make a modification for the usual direct method to find some conditional similarity solutions of a (2+1)-dimensional general nonintegrable KdV equation.

Recently, a new decomposition of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation to a (1+1)-dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.

We have proposed a quantum system with equally-distant partially-entangled alphabet states which has the minimal mutual overlap and the highly distinguishability, these quantum states are used as the “signal states” of the quantum communication. We have also constructed the positive operator-valued measure for these “signal states” and discussed their entanglement properties and measurement of entanglement. We calculate the accessible information for these alphabet states and show that the accessible information is closely related to the entanglement of the “signal states”: the higher the entanglement of the “signal states”, the better the accessible information of the quantum system, and the accessible information reaches its maximal value when the alphabet states have their maximal entanglement.

A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the mean first-passage time is calculated by the use of two approximate methods, respectively. It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity; (ii) a minimum occurs on the curve of the second-order moment of the system vs. noise intensity at the point D_Γ=0.025; (iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time τ, while the conventional steepest descent approximation leads to poor results.

The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin-Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.

This paper is devoted to the one-loop calculation of the fermion Green function in QED within the framework of the minimal quantization method, based on an explicit solution of the constraint equations and the gauge-invariance principle. The relativistic invariant expression for the fermion Green function with correct analytical properties is obtained.

In this paper we study the spinor constructions of gauge fluxes and Ramond-Ramond fields on noncommutative tori T^d up to d=6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced. So that we can express the Chern-Simons Lagrangian in toroidal compactification as a product of spinors.

We discuss the anomalous magnetic moment of muon in the minimal supersymmetric model with and without right-handed neutrinos. In the same framework, the decay width of τ→μγ is also evaluated. Considering the measured g-2 value of muon in the E821 experiment and other experimental constraints on the lepton-flavor-violation processes, we carry out numerical analysis on the concerned observables in the minimal supergravity scenario.

The decay process J/ψ→p+X, X→p+P, where p,p and P are the proton, antiproton and pseudoscalar states, respectively, has been studied in terms of the angular distribution and the generalized moment analysis methods. The result shows that we can identify the spin, but cannot determine the parity of the baryon resonance state X produced in the process J/ψ→p+X, X→p+P.

The adiabatic effective baryon-baryon interactions and dibaryon candidates are studied systematically with three constituent quark models based on different effective degrees of freedom: Glozman-Riska-Brown Goldstone boson exchange model based on constituent quark and Goldstone boson coupling; Fujiwara model based on constituent quark gluon coupling and Nijmegen one-boson exchange; QDCSM based on constituent quark and gluon coupling with quark delocalization and color screening. We find that the three models predicted the similar effective baryon-baryon interactions for roughly two thirds among the 64 states consisted of octet and decuplet baryons. The differences among three models and their separate characteristics are also studied.

In the framework of topcolor-assisted technicolor model we calculate the contributions from the pseudo Goldstone bosons and new gauge bosons to e⁺e^-→tt. We find that for reasonable ranges of the parameters, the pseudo Goldstone bosons afford dominate contribution, the correction arising from new gauge bosons is negligibly small, the maximum of the relative corrections is ～10% with the center-of-mass energy √(s)=500 GeV; whereas in the case of √(s)=1500 GeV, the relative corrections could be up to 16%. Thus large new physics might be observable at the experiments of next-generation linear colliders.

The K⁺ scattering cross section with the in-medium virtual pion is evaluated in the lowest-order chiral perturbation theory with the density-dependent pion decay constant and mass. The contribution of nuclear pions to the total K⁺-nucleus cross section is found to be about 5% and 12% when the excess pion numbers per nucleon n_π=0.057 and 0.13 are used. The inclusion of the off-mass-shell behavior of the K⁺π amplitude produced a significant improvement in the K⁺-nucleus cross section.

The B-spline basis set method is used to study the properties of helium confined endohedrally at the geometrical centre of a fullerene. The boundary conditions of the wavefunctions can be simply satisfied with this method. From our results, the phenomenon of “mirror collapse” is found in the case of confining helium. The interesting behaviors of confining helium are also discussed.

The classical molecular dynamics simulation has been used to study the equation of state of gas H₂, D₂ and T₂. It has also been investigated that the isotope mass affects on the accuracy of equation of state. Our calculated results show that the classical effect is principal and the isotope mass effects on the equation of state are obvious for the much light gases. At the same time, some useful theoretical data of equation of state for these gases have been provided. It is found that the classical simulation is still effective to the quantum gas. However, the quantum mechanics simulation and the improvement of intermolecular interaction potential are necessary if more accurate computational results are expected.

The equipartition of energy applied in binary mixture of granular flow is extended to granular flow with non-uniform particles. Based on the fractal characteristic of granular flow with non-uniform particles as well as energy equipartition, a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived. Thermal conduction resulted from motions of particles in the granular flow, as well as the effect of fractal dimension on effective thermal conductivity, is discussed.

In the framework of nonperturbative quantum field theory, the critical phenomena of one-dimensional extended Hubbard model (EHM) at half-filling are discussed from weak to intermediate interactions. After the EHM being mapped into two decoupled sine-Gordon models, the ground state phase diagram of the system is derived in an explicit way. It is confirmed that the coexisting phases appear in different interaction regimes which cannot be found by conventional theoretical methods. The diagram shows that there are seven different phase regions in the ground state, which seems not to be the same as previous discussions, especially the boundary between the phase separation and condensed phase regions. The phase transition properties of the model between various phase regions are studied in detail.

Zero-temperature Monte Carlo simulations are used to investigate the hysteresis of a magnetic particle in a dipolar Ising model. The magnetic particle is described in a system of permanent dipoles, and the dipoles are located in a cubic lattice site. The effects of the shape and the size of the particle on the hysteresis loop at zero temperature are obtained. For strong exchange interactions, the shapes of magnetic hysteresis loops approach rectangle. For weak exchange interactions, the effects of the size and the shape of the particle on the loops are more remarkable than those of strong exchange interactions case. The slope of the hysteresis loop decreases with the increase of the ratio of the semi major axis to the semi minor axis of the ellipsoidal magnetic particle, and there is an increase of the slope of the hysteresis with the decrease of the size of the magnetic particle. The effects of the shape and size of the particle on the coercive force at zero temperature are also investigated.