In coherent state representation and in the absence of rotating wave approximation,the analytical forms of the eigenenergies and eigenfunctions of a trapped ultracold ion interactingwith a travelling wave laser are presented for some particular detunings. The differencebetween the standing wave laser and the travelling one radiating a trapped ultracold ion isalso pointed out.

In addition to the well-known quantum numbers, the total spin as a good quantumnumber has also been introduced to classify the eigenstates of the H₃⁺-like systems. Thedegeneracy of the ground state and the structures of the ground rotation bands have beendeduced based on an ab initio symmetry consideration.

The effects of pressure on the doped Kondo insulators (KI) are studied in theframework of the slave-boson mean-field theory under the coherent potential approximation.A unified picture for both the electron-type KI and hole-type KI is presented. The density ofstates of the f -electrons under the applied pressures and its variation with the concentrationof the Kondo holes are calculated selficonsistently. The specific heat coefficient, the zerotemperaturemagnetic susceptibility as well as the low-temperature electric resistivity of thedoped KI under various pressures are obtained. The two contrasting pressure-dependent effectsobserved in the doped KI systems can be.naturdy explained within a microscopic model.

We extend a previous result of ours [G.S. Tian, Phys. Rev. B58 (1998) 76121 on the charged gap and the spin-excitation gap of the half-filled Kondo lattice model to the doubleexchange model. In our original approach, this model cannot be dealt with since its localized spins have a large spin number S=3/2. By following a construction argument due to Zener and rewriting the double-exchange Hamiltonian, we are able to overcome this difficulty and re-establish the same relation for this model.

By using strong-field scheme, the complete d⁵ energy matrix with symmetry has been constructed. Then, by diagonalization of this matrix at normal and various pressures,the whole energy spectrum [including the ground-state zero-field splitting (GSZFS)] and its pressure-induced shift (PS) of Znlb:Mn²⁺ have uniformly been calculated. The results are in very good agreement with experimental data. According to the eigenfimctions and PS, the assignments of four absorption bands have been given. By taking into account the dect of different deformations of t₂ and e radial wavefunctions on t₂³(⁴A₂)e²(³A₂)⁴ A₁ and t₂³(²E)e²(³A₂)⁴E, the position of the third absorption band at normal pressure has been estimated.The tetragonal field is important for GSZFS of ZnTe:Mn²⁺ and its PS, which supports the existence of tetragonal Jahn-Teller distortion in ZnTe:Mn²⁺ The physical essentials of typical levels, GSZFS and their PS have been revealed.

The effective mass mismatch of a conduction band electron in a semiconductor.superlattice renormalizes the electron confining potential. Taking this effect into account we calculate the absorption coefficient of the intraband optical transition in an InGaAs/InAlAs superlattice. We find that the electron effective mass mismatch causes a notable broadening of spectrum linewidth, which can well account for the experimental result.

A tight-binding effective potential has been employed, in conjunction with a genetic algorithm, to fully optimize the Cr₁₃ cluster geometry without imposing any symmetry constraints. The minimum energy structure of this cluster is found to be a slightly distorted icosahedron. Based on the optimized structure and three assumed geometries (icosahedron,bcc-like and fcc-like), the structural dependence of electronic and magnetic properties of the Cr₁₃ cluster is discussed by using a d-band Hubbard-like Hamiltonian in the unrestricted Hartree-Fock approximation. Results are given for the average magnetic moment and local magnetic moments. It is found that for all considered geometries the Cr₁₃ cluster exhibits antiferromagnetic behavior. Results are also given for the cohesive energy, average coordination number, and local electronic densities of states. The results indicate that the average coordination number per atom in the cluster geometry is a significant factor to affect the magnetism.Also, the local density of states is a sensitive function of geometry.

A single-spin transitional critical dynamics based on the Glauber theory is used to investigate the d-dimensional kinetic S⁴ model. We derive the fundamental dynamical equations by a cumulant expansion, and then, a one-dirnensional model is treated. We obtain approximately the local magnetization and equal-time spin-pair correlation function, in which the terms of k₃ and the higher orders are ignored (corresponding to high-temperature cutoff). These are finally extended to d-dimensional case. In addition, we obtain the critical point k_c of d-dimensional S⁴ model, and give a relation satisfied by the dynamic critical exponent Z and the correlation length critical exponent ν.

The mobility of a,one-dimensional damped fienkel-Kontorova chain under a dcdriving force is studied numerically and analytically. For the commensurate case, the particles in the chain are synchronized at high driving force. For the incommensurate chain, a single mode solution dominates at high mobility regime. We are able to calculate the mobilities for both the cases analytically, and a good agreement with numerical results is found. The mobility hysteresis for the incommensurate chain is explained by the existence of two branches of physical solutions, and transitions occur when one of them breaks up.

We consider a two layered neural network in which the second layer is composed of simple pulse-coupled neuronal oscillators connected by excitatory and inhibitory lateral interaction weights. For storing information' a self-organizing learning algorithm with respect to the amplitude of the neuronal oscillators is introduced. The dynarnical behavior and the retrieval ability of information of this model are analyzed. Computer simulation shows that the learning can enhance the coherent characteristic of the neuronal activities and the dynamical behaviors of this model in pattern recognition are similar to the dynarnical process in biological neural system and perform information retrieval property to stored patterns.

A Gaussian white noise model and a symmetric dichotomous noise model for a three-Josephson-junction device are studied. It is shown that the symmetric noise can produce net voltage (Its corresponding dc current is zero), which sterns from the multiplicative noise,the asymmetry of the potential or the asymmetry of the potential itselt; respectively for the Gaussian white noise model or for the dichotomous noise model. The net voltage is negative,and exhibits a peak with increasing the additive noise strength (the stochastic resonance). The dc current-voltage characteristics are calculated for the two models. In addition, we find that when the dc current is not zero, in some scope the absolute value of the dc voltage versus the additive noise strength also presents the stochastic resonance.

We propose a dynamical elliptic algebra which is based on the relations RLL = LLR^*, where R and R^* are the dynamical R-matrices of A_n-1⁽¹⁾-type face model with the elliptic module shifted by the center of algebra. nom the high-rank Gauss decomposition,h we obtain the Drinfeld currents of dynarnical elliptic algebra .

A conformal-invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimensions is proposed. Taking the compound KdV-Burgers (cKdVB) equation and the KdV-Burgers (KdVB) equation as concrete examples,we obtain many new conformal-invariant models with Painleve' property and the approximate solutions of the cKdVB and KdVB equations. In some special cases, the approximate solutions become exact.

Based on the self-consistent scheme beyond the mean-field approximation in the large N_c expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of N_c,an approximate internal meson propagator is deduced, which is in order of O(l/N_c). In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show that, different &om the mean-field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond the meanfield approximation.

The spin-isospin-dependent response function of nucleus is studied in the relativistic formalism. Besides the well-known relativistic particlehole and A-hole excitations, the antiparticle excitations such as nucleon-antinucleon, nucleon-antidelta, antinucleon-delta excitations are also taken into account in the calculation of the response function, and the effect of the antiparticle excitation is emphasized. The antiparticle excitation enhances the response function and its effect to the response function is largely determined by the cutoff parameter which is introduced by the need of the renormalization. The position of the peak of the A-hole resonance is mainly dominated by short range correlation Landau-Migdal parameter g', and we find g' is about 0.6. The effect of two-nucleon absorption and projectiletarget form factor are also studied.

The Nambu-Jona-Lasinio model,is extended to inclusion of the nonlocal effective quark interaction with confinement. An effective Hamiltonian in the instantaneous approximation is used to study meson properties in the random phse approximation.

We investigated the Drell-Yan process of the light neutralino pair (i, j = 1, 2) productions at hadron colliders. We studied the dependence of the coupling properties of two light neutralinos on, three SUSY Lagrangian parameters M₁, M₂ and μ, and find that the production rate of pair will be dominated by the Higgsino-like couplings under the conditions p << M₂ and μ～M₁.

We demonstrate that if the universe is dominated by the massive cold dark matter, then besides the generally believed thermal distribution of the dark matter relics, there may exist some very energetic nonthermal relics of the dark matter particles in the universe from some unknown sources, such as from decay of supermassive X particle released from topological defect collapse or annihilation. Very interesting, we point out that these high energy dark matter particles may be observable in the current and future cosmic ray experiments.

We present a study of associated J/ψ+γ production through double pomeron exchange at energies reached at the Fermilab Tevatron.and CERN LHC based on the Ingelman-Schlein model for hard difiactive scattering and the factorization formalism of nonrelativistic QCD for quarkonia production. We find that the process p+p→p +p + J/ψ+γ + X can be used to probe the gluon content of the pomeron and study the nature of hard difiactive factorization breaking.

This paper gives a rigorous and explicit calculation of the scattering wavefunction for the case of a bare thin toroidal magnetic flux, i.e. a thin toroidal magnetic flux without toroidal shielding.

A microscopic approach treating the quantum dissipation process presented by Sun and Yu (Phys. Rev. A49 (1994) 592; A51 (1995) 1845) is invoked to construct the wavefunction of the composite system——the model for a harmonic oscillator interacting with a many-oscillator bath under the rotating wave approximation. It shows the back-action of the system on the bath. In particular, the dynamic evolution of the wavefunction for the composite system maintains a factorized form in its wavefunction. In the limited temperature, the reduced density matrix for the system is also calculated to clarify the influence of Brownian motion on the system.

By virtue of the technique of integration within an ordered product of operators we construct the normally ordered operator fiedholm equation. We use it to derive some new operator formulas. For Weyl correspondence, operator fiedholm equation can also be constructed. Some applications of the operator Fkedholm equation are given.

We study the interaction of negative binomial states with two-level atoms. The dynamical evolutions of atomic population inversion, field entropy, Q function, and phase distribution are investigated in detail. The field becomes a superposition of negative binomial states at certain times, and this is confirmed further by its photon number distribution.

We use the Fokker-Planck equation and stochastic differential equations to study the composite system of the cavity field and the excitons under the finite temperature. The conditions for the stability of the system are given. The effect of reservoir phonons on the quadrature squeezing spectra of the output field is discussed by using small fluctuation a pproximation. We find that the perfect squeezing of the output field appear; at two points under the same condition comparing with the case of zero temperature.

Vacuum spacetimes endowed with two commuting spacelike Killing vector fields are considered. Subject to the hypothesis that there exists a shearfree null geodesic congruence orthogonal to the two-surface generated by the two commuting spacelike Killing vector fields,it is shown that, with a specific choice of null tetrad, the Newman-Penrose equations are reduced to an ordinary differential equation of Riccati type. fiom the consideration of this differential equation, exact solutions of the vacuum Einstein field equations with distribution valued Weyl curvature describing the propagation of gravitational impulsive and shock wave of variable polarization are then constructed.

We present a systematic treatment of the linear theory of scalar gravitational perturbations of various matter (including baryons, cold dark matter, photons, massless neutrinos,and massive neutrino) for the flat, open and close universes, concentrating on the treatment of the massive neutrino component which has been either ignored or approximated crudely for the nonflat universe in previous literatures.

We apply the variational cumulant expansion to study the phase transition of a two-dimensional coupled XY-king model. This model can describe several different systems with underlying continuous and & symmetries. We calculate the free energy, internal energy and specific heat to the third-order approximation with the trial action of two variational parameters. A comparison with Monte Carlo data is also presented.

By using Painlevé analysis, we derive the Backlund transformation for the longwave and short-wave resonance equations and their extending systems. Then we take some constraints of the B?ckJund transformation and find some solutions.

We investigated the moving law of the scroll wave filament by perturbation arguments,and obtained that, when the normal direction of scroll wave front curve surface is similar to that of its filament, the normal speed (noted by α ) of the filament is relative not only to the curvature (k) of the filament, but also to that k₁ of scroll wave front curve surface,i.e., a = εD(k -k₁) (where D is diffusional coefficient), and irrelative to the characteristic speed of excitable media. Besides, we also investigated the moving law of the filament along the axis direction, and obtained the similar result to that of Keener's (J.P. Keener, Physica D31 (1988) 269).

Starting from a known Lax pair, one can get some infinitely many coupled Lax pairs.In this letter, we take the well-known KdV equation as a typical example. Using infinitely many symmetries, the infinitely many inhomogeneous linear Lax pairs of KdV equation can be obtained. And considering the Darboux transformations for the KdV equation leads to the infinitely many inhomogeneous nonlinear Lax pairs.

The calculations of the whole energy spectrum of Zns:Ni²⁺ at normal pressure and pressure-induced shifts of its levels have been carried out on the basis of the theory of pressure-induced shifts and the diagonalization of the complete d⁸ energy matrix in a regular tetrahedral field. The calculated results are in very good agreement with experimental data at normal and high pressures. The comparison between the results of ZnS:Ni²⁺ and Mg0:Ni²⁺ indicates that the comlency of ZnS:Ni²⁺ is obviously stronger than the one of MgO:Ni²⁺;the expansion of electron wavefunctions of ZnS:Ni²⁺ under pressure is obviously larger than that of MgO:²⁺; and the pressure-induced shifts of levels of znS:NiZf show strong nonlinearity.

By studying numerically the light transmitting through a finite nonlinear Fibonacci multilayer, we find the gap-soliton-like phenomenon. The Fibonacci multilayer contains a Kerrtype nonlinearity in one component. When the frequency of incident light is in a stop gap, increasing the incident light intensity will make the system switch from a lower transmission state to a higher transmission state. Transmissivity for some frequencies can reach unit, which shows that they correspond to transparent states. Distribution of the field intensity in the Fibonacci structure has a particular gap-soliton-like shape, which has the multi-carrier wave.

The temperature dependence of polaron cyclotron resonance mass in GaAs/AlGaAs heterostructures is reinvestigated theoretically. By taking into account the electron-longitudinal-optic phonon interaction with temperature-dependent many-body effects, the conduction band non-parabolicity, and the influence of nonzero magnetic field, a good agreement with experiment is obtained.

Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.

We examine a quantum Hopfield neural-network model in the presence of trimodal random transverse fields and random neuronal thresholds within the method of statistical physics. We use the Trotter decomposition to map the problem into an equivalent classical random Hopfield-type Ising model and obtain phase transitions between the ferromagnetic retrieval and the paramagnetic phases. The influence of competition between the diluted random transverse fields and the diluted random thresholds on the system is discussed, and some interesting results such as tricritical points and reentrance are analyzed.

A quantum spin Heisenberg model with exchange and single-ion anisotropy is investigated by variational cumulant expansion method. Easy-axis and easy-plane cases are considered separately. Dependence of critical temperature and type of ordered phase on anisotropy parameters are examined in full detail. Thermodynamic functions are calculated for some instances.

It is proven that on a symplectic submanifold the restricted c-KdV flow is just the interpolating Hamiltonian flow of invariant for the restricted Toda flow, which is an integrable symplectic map of Neumann type. They share the common Lax matrix, dynamical r-matrix and system of involutive conserved integrals. Furthermore, the procedure of separation of variables is considered for the restricted c-KdV flow of Neumann type.

The dromion interaction of the (3+1)-dimensional conditional integrable model, Jimbo-Miwa-Kadomtsev-Petviashvilli (JMKP) system, is re-studied by means of the equipotential surface plots. The result shows that the interaction among dromions of the JMKP system is elastic which corrects the conclusion of our previous paper (J. Math. Phys. 38 (1997) 3123). firtherrnore, the interaction is also irrotational. That is to say, there are not exchanges of any physical quantities like energy, momentum and angular momentum.

A unified method to construct the (multi-)boson realizations of the Lie and quantum algebras is proposed based on a universal deformation of boson (Heisenberg-Weyl) algebra and its multiboson realization. Some explicit examples, the Lie algebras sl(2) and su (Ill), q-boson algebra, quantum algebras sl(2)_q and su (l,l)_q, along with the q-ladder algebra are studied in detail. In particular, the square boson realizations of su (1,l) and su (l,l)_q are naturally obtained as special cases.

A new noncommutative differential calculus on function space of discrete Abelian groups is proposed. The derivatives are introduced with respect to the generators of the groups only. It is applied to discrete symplectic geometry and Hamiltonian systems with H(p, q) = T(p) + V(q) as well as the lattice gauge theory on regular lattice.