Introducing the Dyson-Maleev transformation and the coherent state ansatz, we obtain two partial differential equations of motion in antiferromagnet RbFeCl₃. Employing the method of multiple scales and the long-wavelength approximation, we reduce these equations in to a nonlinear Schrödinger equation. By making use of inverse-scattering transformation, we obtained the nonlinear excitations in an tiferromagnet RbFeCl₃.

The thermal shift of crystal field spectra of rare earth or transition metalions includes four contributions of different characteristics. In this paper we develop a theory of calculating all those contributions in detail. The contributions to thermal shift consist of that of thermal expansion and those of electron-phonon interaction. The thermal shift caused by thermal expansion is interpreted and calculated by making use of theory of pressure-induced spectral shift. The contribution of phonons of optical branches is given by using single frequency model. The contributions of phonons of acoustic branches include two terms, which are derived by taking into account contributions of all the Γγ in electron-phonon interaction.The theoretical form'ulas for parameters in the most important term are given.

A quantum antiferromagnetic system on the Kagomé net with periodic boundary conditions is studied using numerical diagonalization techniques. We study clusters of sizes 9, 12, 15, 18, 21 spins (see Fig.1), which has been used in a similar study in Ref.[1]. We found that the lowest excitations are not the usually expected spin flipping excitations. The smooth decrease of the excitation energy with the increase of system sizes indicates the existence of soft modes in the thermodynamic limit. For systems with odd number of spins, the ground states are multiply degenerate. The number of degeneracy is twice that of the classical planar model.

A new nonfree d-orbital for the transition metal ion in octahedral site symmetry crystal is proposed by considering the ligand charge penetration. The quantitative relationship between the nephelauxetic decreases of Racah parameters B, C, spin-orbit coupling parameter ξ_d and the corresponding crystalline parameters is established by using a simple point-charge model. The d-orbital is applied to calculation of the d-d transition and g-factor of the Ni²⁺ ion in nickel-silver thiocyanate. The calculated results are in good agreement with experimental findings.

We present a simple, general method for calculating the binding energies of excitons in semiconductor quantum wires. The binding energy is given by an integral (over the electron and hole two-dimensional coordinates perpendicular to the wire) of a prescribed function weighted by the squares of the electron and hole subband envelope functions. Taking as an example, we calculate the binding energy of exciton in quantum wires assuming an infinite confining potential. This method should be applicable to a variety of more complex systems.

The form of the universal scaling law of the critical dynamic exponent, z = D_ƒ + 2/υ, is found on a family of regular fractals by the exact TDRG method. Here, we generate a regular fractal by an anisotropic growing process. Identifying the growing probabilities as the interactions between Ising spins on the fractals, we map the growing probability clouds as a group of the anisotropic Ising Hamiltonians. Applying the RG transformations, we find that the systems of this group of Ising Hamiltonians can be described by two universal static correlation exponents υ₀ = ∞ and υ = 1. So, the growing processes proposed by us capture the essential features in the directed DLA simulations. The studies about their critical dynamic behaviours reveal that unlike the one-dimensional chain the critical dynamics of the kinetic Ising model on the regular fractals is universal. The further discussions show that there is a universal scaling law form of the critical dynamic exponent of the kinetic Ising model, z = D_ƒ + R_max/2υ, on the site models of the regular fractals with R_min = 2. Meanwhile, we discuss Daniel Kandal's correction to the formula of the,critical dynamic exponent in the TDRG method and show that our TDRG calculations are exact.

The general quartic map is studied by symbolic dynamics in the three parameter space, joints are obtained in terms of the kneading theory. We describe the skeleton of superstable. kneading sequences corresponding to a joint and all allowed superstable kneading sequences in the kneading space in details. A criterion for the existence of chaos has been given according to the topological entropy.

In this paper, we considered a q-superoscillator model and constructed a transformation matrix which transforms the-usual algebra of q-boson and q-fermion operators of the qsuperoscillator into a nonlinear shift automorphism algebra. The q-supercoherent states for the q- superoscillator model is introduced by utilizing the transformation matrix. They are compared with the coherent states defined as eigenstates of the annihilation operators. Matrix elements of the transformation matrix on the Fock space bases are evaluated as well.

In this paper, quantum subgroups and quantum co-set spaces including corresponding dififerential calculi are discussed.

A perturbation theory for the MNLS equation with corrections based upon the inverse scattering transform is applied to the description of soliton evolution in the presence of permanent perturbation. In the case of a simple pole of the transmission coefficient, we investigate three main effects due to small perturbation: 1) a slow change of soliton parameters; 2) a deformation of its shape; 3) the formation of a soliton tail. We give in detail all the formulae which are necessary for further dealing with practical problems in nonlinear fiber optics (especially in femto-second region) and in nonlinear Alfven waves.

The finite Dirac's contact transformation according to Dirac's physical idea is obtained. It is shown that its generators belong to the smallest evolution closed subalgebra of the first class constraints but do not exhaust all the first class constraints in general. Then the extended Dirac's conjecture is proposed and is applied to Cawley's counter example of Dirac's conjecture successfully.

The Gaussian wave-functional approach is used to variationally study the two-particle states of the sinh-Gordon and sine-Gordon fields in (1+1) dimensions. We find that in the sine-Gordon model there exist two-particle bound states for a certain range of the coupling constant, where the vacuum state is stable, and in the sinh-Gordon model there are no twoparticle bound states. The scattering behaviour of both models has also been investigated in detail.

The non-equilibrium processes of quark-gluon-plasma (QGP) in the coexistent phase of first order phase transition are studied under Lee's model. Both the classical and the quantum transport equations of quark as well as the corresponding hydrodynamical equations are obtained. The classical transport equations are deduced from the quantum ones in the semiclassical limit, showing that the theory is self-consistent. The transport equations of gluon in the semi-classical limit and the equation for the fluctuation of gluon distribution function under the condition of near-equilibrium are also derived.

We propose and study a new kind of superposition states: even-and odd-displaced squeezed states, defined as [D(z)+D(-z)]S(γ)|0> and [D(z)-D(-z)]S(γ)|0>, which are characteristic of possessing even and odd photon numbers respectively. We find that the even-displaced squeezed state may exhibit stronger squeezing than that of the ordinary squeezed state D(z)S(γ)|0>.

We discuss anomalous d=2 non-Abelian chiral theory with minimal Wess-Zumino-Witten (WZW) action. The Schwinger terms between Gauss-law constraints G^a(x) and G^b(y) can not be canceled by the minimal WZW action. If we define modified Gauss-law constraints G_m^a(x), the Schwinger terms between the constraints G_m^a(x) and G_m^b(y) disappear, the constraints G_m^a(x) become the first-class ones. And the total action S(A, U, G) is gaugeinvariant. When we choose the unitary gauge G = 1, the non-Abelian chiral theory with the generalized faddeevian regularization scheme is gained. And the relation between faddeevian and usual regularization can be obtained.

Periodic modulating soliton solutions to Boussineq equation are obtained by the bilinear transformation method. Their various variants are discussed.

In this letter, we discuss the quantum superalgebra OSP_q(l,4). With the help of the SU_q(2)×U(1) basis, we construct two types of representations for the quantum superalgebra, called the-1/2-representation and the 1/2-representation. Both of them are infinitedimensional.

A grade adjoint operation for the boson and fermion operators is considered. A graded bosonfermion algebra is constructed. Explicit expressions for the generators of the osp(2,l) and spl(2,l) superalgebras in terms of suitable pairs of graded boson and fermion operators are given. Infinite-dimensional grade star representations are obtained.

Through the explicit calculation to the Gaussian effective potential in the sine-Gordon model in (1+1) dimensions with the normal-ordering prescription of renormalization, we find that the "m" in Coleman's formalism in operator notation can be regarded as the renormalized mass.

In this paper, the high-order perturbation theory for rearrangement collision in the presence of an intense external field is derived. An extended Kroll-Watson formulg for high-order rearrangement collision is obtained. The results suit any three-body rearrangement collision and any form of two-body interaction potential. The low-and high-frequency approximations are discussed.

A path integral method is used to study the time evolution of a three-dimensional timedependent system. The propagator for a charged particle in a time-dependent magnetic field and quadrupolar electric potential is obtained.

We study the effects of screened Coulomb electron-electron interactions in halogen-bridged. mixed-valence transition metal linear chain complexes (MX chains) applying lattice model with a double-well potential to simulate CDW ground state. With the periodicity of MX chain, we construct a complete set of orthogonal and normalized wave functions in view of the second-neighbor approximation. Starting from the restricted Hartree-Fock scheme, we diagnolize the Fock matrix analytically and calculate the LCAO-MO-SCF solutions. Our theory shows the dependence of charge transfer on the strength and screened coefficient of electron-electron interaction.

A generalized mixed spin model with anisotropic interactions is considered on the union jack lattice. We find that the model is equivalent to a free fermion model. The critical temperature is obtained. In special cases, we get the same results as exact solutions.

By making use of the theory for thermal shift of crystal field spectra of rare earth or transition metalions, taking into account all the contributions adequately, we calculated R line thermal shift of MgO:Cr³⁺ by fitting experimental data. The results show a good agreement with thermal shift experimental data and a series of other experimental data of MgO:Cr³⁺. Values of the most important parameters are calculated theoretically with wavefunctions obtained from diagonalization of complete d³ energy matrices. They are in good agreement with those from fitting experimental data.

The spin-1/2 antiferromagnetic Heisenberg mode (AFHM) is investigated on the triangular lattice by using a general Bose transformation for magnetic system. We considered both thedynamical and kinematical interactions. Our calculation of the ground state energy showssome evidence which is favorable for the absence of sublattice long-range order on triangularLattice.

We study a set of nonlinear stochastic equations describing a large class of nonlinear mul-tidimensional non-Markovian dynamical systems driven by additive O-U noise, and a classof nonlinear multidimensional differential equations driven by dichotomous noise. By virtueof the stochastic generalization of usual adiabatic approximation, the equations for the orderparameters are obtained. The statistical properties of the new stochastic variables arestudied.

For the NLS equation with nonvanishing boundary condition, Hamiltonian formalism is developed. Together with two previous works, the results obtained are in the same level as those obtained for the NLS equation with vanishing boundary condition.

By the direct method that involves no group theory, the Davey-Stewartson equations (DSE's)in (2+1) dimensions have been reduced to some (1+1)-or 2-dimensional partial differentialequations which have included all the types of symmetry reductions using the standard Liegroup theory. As a special case we obtained the 1-dimensional reducing equations fromDSE's in (2+1) dimensions directly.

The correlations among the radius, lifetime and coherent parameter of the pion source in high energy heavy-ion collisions are analyzed. The effects of q₀ cuts on the radius are studied. The reason why the data of 4π detector is not sensitive to the lifetime is also discussed.

By means of the finite temperature and finite density real time Green's function method, the effective mass of sigma meson is calculated by summing the bubble diagrams. It is found that the formula of effective mass given by ρ meson can also be used to describe the sigma meson, but the parameter n depends on density. The conjecture of Brown and Rho about the effective mass of meson can well be proved by quantum field theory in high temperature region.

The cumulant expansion of U(1) lattice gauge model at finite temperature (N_T=1) to the sixth order is presented. The variational parameters are determined by requiring thatthe corrections to the zeroth order approximation are the smallest. The order parameter,Polyakov line , converges well and is in good agreement with Monte Carlo simulations.Especially, the deconfinement phase transition point can be determined with accuracy.

Padé Approximants are applied to the β-functions given in perturbative forms in λØ⁴ and QED in order to improve their convergence and to go beyond perturbation. Then we integrate the β-functions to find the solutions of the effective coupling constants. Some discussions on the results are given.

With the aid of generating-functional technique, the many-body correlation dynamics wasgeneralized to the relativistic cases within a Green's function formalism and two sets of equations of motion for the correlation (or connected) Green's functions were derived respectively for the scalar س-model and the Yukawa model, which were nonperturbative in nature and could provide physically transparent truncations with respect to the order of correlations.

Incorporating the nonpkrturbative effects of QCD, an effective potential with confinementterms is derived. With it, we calculate the spectrum of the cc family and also evaluateΓ_e+e-,1³ P_J splitting and the electromagnetic transition rates. The results show that as theBorelization is taken, one can obtain values which are roughly consistent with experimentaldata, whereas without the Borelization the values are quite apart from the data. In theprocess of calculations, there are few free parameters, therefore the obtained results are ofsignificance for understanding the underlying theory of the potential model.

We study the infinite U Hubbard model on a square lattice. By introducing a transformationwhich transforms the up spin and down spill fermions in to two families of bosons with phasefactors, we show that the fully ferromagnetic state is not the ground state at any finite holeconcentration.

The statistical distribution for a system of q-deformed harmonic oscillators is studied and an explicit form of q-dependence of the distribution function is given. The physical meaning of the deformation parameter q is discussed.

In this short communication we show that the new Lax pair for SDYM theory can be derivedfrom prolongation approach and some equivalent expressions for SDYM integrable theoryare given by the "gauge" transformation.

Using the method introduced by Clarkson and hiuskal (CK) recently, we obtain the similarity reductions of the fifth order KdV equation, and give some discussions of special casesat last.

In this letter, we present a set of new formulas of three q-generators of quantum algebraSU_q(2), which are the nonlinear combination of the basis elements of Lie algebra su(2). Inthe limit q → 1, these q-generators contract to the quantities that satisfy the commutationrelation of Lie algebra su(2).

Using the technique of integration within an ordered product (IWOP) of operators we findsome new continuum state vectors which span completeness relations in niulti-mode Fockspace. This fact tells us that the representation theory in quantum mechanics need to bestudied in more detail.