When two representations of the Lie algebra are coupled, the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states. These kernels have a connection with usual coupling coefficients. The explicit expressions of these kernels for SU(2), SO(4) and SU_q(2) are given. When the direct product of three representations is formed in two ways, the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced, and the relations between these kernels and the general recoupling coefficients are obtained. The properties of these kernels are discussed.

Using every realization of the Virasoro-type symmetry algebra [σ(f₁), σ(f₂)]=σ(\dot f₁f₂-\dot f₂f₁), we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many (3+1)-dimensional equations which possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebras are obtained.

The relation between one-to-one correspondent orthonormal eigenstates of H⁰ and H(λ)=H⁰+λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H⁰, the relation between one-to-one correspondent orthonormal eigenstates |φ_i(λ)〉 and |φ⁰_m(i)〉 can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.

A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.

The two-dimensional gravity model with a coupling constant k=4 and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.

Through adding a nonlinear self-feedback term in the evolution equations of neural network, we introduced a transiently chaotic neural network model. In order to utilize the transiently chaotic dynamics mechanism in optimization problem efficiently, we have analyzed the dynamical procedure of the transiently chaotic neural network model and studied the function of the crucial bifurcation parameter which governs the chaotic behavior of the system. Based on the dynamical analysis of the transiently chaotic neural network model, chaotic annealing algorithm is also examined and improved. As an example, we applied chaotic annealing method to the traveling salesman problem and obtained good results.

The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT). Using this method, wavefunctions are approximated by linear combination of graphs consisting of only one connected Wilson loop. We study the excited state energy and wavefunction in (2+1)-D SU(3) LGT up to the third order. The glueball mass shows a good scaling behavior.

The transverse Ward-Takahashi (W-T) relation for the vector vertex in quantum field theory is derived by calculating the curl of the time-ordered product of the three-point function including the vector current operator. This provides the constraint on the transverse part of the vertex. By combining the transverse and normal (longitudinal) W-T identities, we obtain the expression for the full vector vertex function.

The contribution of color-octet heavy quarkonium production mechanism in P+Fe→J/ψ+γ+X process is calculated and discussed. The results show that color-octet contributions are rather large and sometimes can exceed the color-singlet contributions. Using the structure function of Fe given by double Q²-rescaling model, the influence of nuclear effect on this process is also studied.

We calculate the corrections of extended technicolor (ETC) interactions to the asymmetry parameter A_LR and the polarized parameters P_L^t, P_R^t of the process e⁺e^-→ tt in topcolor-assisted multiscale technicolor model. Our results show that the ETC effect on P_R^t is negligibly small which can be safely ignored, and the ETC effect on A_LR may be testable at high energy e⁺e^- linear collider (LC). For 0.03≤ε≤0.1, 500 GeV≤(s)^1/2 ≤800 GeV, the relative correction of P_L^t is in the range of 15%≤δP_L^t/ P_L^t,SM≤39%, which will certainly be detected at the LC experiments (for example TESLA).

We give the moment expressions for the boson resonances X with spin-parity J_X^P_XC=0⁺⁺, 1^-+, 1⁺⁺ and 2⁺⁺ possibly produced in the process J/ψ→ρX, X→b₁(1235)π, b₁→ωπ in terms of the generalized moment analysis method. The resonance with J_X^P_XC=1^-+ can be distinguished from other resonances by means of these moments except for some rather special cases. The suggestion that the search for the hybrid with I^G(J^PC)=1^-(1^-+) can be performed in the decay channel J/ψ→ρωππ at upgraded BEPC/BES is presented.

The difference of τ_B and τ_Λb indicates the role of the light flavors. We calculate the lifetimes of B-meson and Λ_b based on the weak effective Hamiltonian while assuming the heavy baryon is constructed by a heavy b-quark and a diquark containing two light quarks. In this scenario, we use the information of the measured ratio τ_Λb/τ_B as input to predict rates of the inclusive weak decays of Σ_b^(*) and Ξ_b^(*) into non-bottom final states. We find that these rates of Σ_b^(*) and Ξ_b^(*) are much larger than those of B-mesons and Λ_b. We also give the predictions for the lifetimes of Ω_b and Ω_b^*. Phenomenological implication of our result is discussed.

We in terms of optical theorem estimate the lifetime of B_c meson with the parameters which are determined by fitting the data for the lifetimes and inclusive semileptonic decays of various B and D mesons. In the estimation, we find that the bound-state effects are important, and take them into account carefully in the framework which attributes the effects to the effective masses of the decay heavy quarks in the inclusive processes. We also find that to B_c lifetime the penguin contribution is enhanced due to possible interference between the penguin and the ‘tree part’ c₁O₁+c₂O₂.

The strange hadronic matter with nucleons, Λ-hyperons and Ξ-hyperons is studied by using an effective nuclear model in a mean-field approximation. The density and strangeness fraction dependence of the effective baryon masses as well as the saturation properties and stabilities of the strange hadronic matter are discussed.

The excitation function for the fission of ²³⁰Th induced by neutrons has an unusual maximum for neutron energies in the vicinity of 700 keV. It has been suggested that this maximum may be associated with the vibrational-mode resonance states. The unusual peak in the excitation function is interpreted in terms of a vibrational-mode resonance state in a two-humpted fission barrier. From theoretical fits to the fission cross sections and angular distributions, it is shown that the resonance has K=1/2.

A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyperspherical harmonic method. This approach is numerically competitive with the variational methods, such as that using the Hylleraas-type basis functions. Numerical comparisons are made to demonstrate the efficiency of this approach, by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom. The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in this paper and the true wavefunction. This full matching was not reached by most other methods. For example, the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock. Two important approaches are proposed in this work to reach this full matching: the coordinate transformation method and the asymptotic series method. Besides these, this work makes use of the least square method to substitute complicated numerical integrations in solving the Schrödinger equation without much loss of accuracy, which is routinely used by people to fit a theoretical curve with discrete experimental data, but here is used to simplify the computation.

By means of the Bloch-Maxwell equation, the Raman interaction of a trapped ultracold ion with two traveling wave lasers is treated semiclassically. As the model works without limitation of the Lamb-Dicke limit and the weak excitation regime, we study chaotic behavior of the system in the wide range of the parameters. It is shown that the chaotic behavior is more and more pronounced with the increase of the Lamb-Dicke parameter and Rabi frequency, and can be exhibited experimentally by using quantum jump technique.

We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results are interesting. For example, if the wave packet is very narrow or/and the interaction is very strong, no matter the atom is initially in its ground state or excited state, the atomic inversion approaches zero as time approaches infinity. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is an even function, then the atomic inversion equals zero at any time.

The statistical properties of a homogeneously broadened ring laser with an injected signal are investigated and the normalized two-mode intensity auto- and cross-correlation functions are calculated by a full saturation laser theory with backscattering. The theoretical predictions are in good agreement with the experimental measurements. Further investigation reveals that the backscattering can reduce the fluctuations in the system while the full saturation effect plays a major role when the laser is operated above threshold. It is also quite important to notice that the injected signal can drive the weak mode from incoherent light to coherent light.

We discuss the unitary operator corresponding to the general two-mode coordinate-momentum mixed transformation (q₁,p₂)→ (Aq₁+Bp₂, Cq₁+Dp₂), where A, B, C and D are arbitrary real numbers. Suitably selecting the parameters A, B, C and D, we obtain a new two-mode bosonic realization of the SU(1,1) Lie algebra. We also study the squeezing effects of the squeezed vacuum associated with the new two-mode bosonic realization of the SU(1,1) Lie algebra. The results show that the new squeezed vacuum does not possess second-order squeezing, but exhibits higher-order squeezing.

On the assumption that a Cooper pair acts as a Bose particle and based on the newly established 〈η| representation, which is the common eigenvector of two particles' relative position and total momentum, we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator. The number-difference-phase uncertainty relation can then be set up, which implies the existence of Josephson current.

We adopt an algebraic method to study the two-mode two-photon Jaynes-Cummings model governed by the Milburn equation and find an exact solution of Milburn equation of the system. The influence of the intrinsic decoherence on the nonclassical effects of the system is also discussed.

We numerically study the propagation, reflection and collision of soliton-like pulses in the vertical granular chain under gravity. For the pure granular chain system, during the propagation and reflection processes at the fixed end, it behaves like a particle. When it is reflected at the free end, it behaves as neither particle-like nor wave-like. When the strengths of the two colliding soliton-like pulses are close, they collide just like particles. When their strengths are greatly different, they collide just like waves. For the soliton behavior in the collision process, from particle-like to wave-like, there is a critical value Θ_C for the ratio Θ of the strengths of the two initial pulses. For the two-layer granular chain, if the mass of the grains in the second layer is less than that in the first layer, the soliton-like pulse in the first layer usually excites about [1/m] soliton-like pulses in the second layer.

The adsorption of O on Ru(0001) is studied by means of Monte Carlo simulation of lattice gas model on a triangular lattice. A recent STM study shows that at low coverage the p(2×2) structure grows via island formation but the p(2×1) structure is abruptly formed at a critical coverage. Moreover, it also shows that there is a coexistence of the p(2×2) and p(2×1) structures. The above results seem not to coincide with the former studies of the system by both the LEED and Monte Carlo simulation. We therefore carried out the Monte Carlo study for the system again in the present paper and found that our simulation almost agrees with the results of the STM.

We study the hybrid exciton-polaritons in a bad microcavity containing the organic and inorganic quantum wells. The corresponding polariton states are given. The analytical solution and numerical result of the stationary spectrum for the cavity field are finished.

We investigate the phase coherent transport in a single channel system. The theory that the transmission zeros lead to abrupt phase change and in-phase resonances is confirmed numerically in two tight-binding models. After calculating the eigenvalues and eigenvectors of the Hamiltonians we also confirmed that the same symmetry of the eigenvectors also leads to the abrupt phase change and in-phase resonances that equal the transmission zero.

The early universe inflation is well known as a promising theory to explain the origin of large-scale structure of universe and to solve the early universe pressing problems. For a reasonable inflation model, the potential during inflation must be very flat, at least, in the direction of the inflaton. To construct the inflaton potential all the known related astrophysics observations should be included. For a general tree-level hybrid inflation potential, which is not discussed fully so far, the parameters in it are shown how to be constrained via the astrophysics data observed and to be obtained to the expected accuracy, and to be consistent with cosmology requirements.

The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the U_n representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.

Discrete breathers are generic solutions for the dynamics of nonlinearly coupled oscillators. We show that discrete breathers can be observed in low-dimensional and high-dimensional lattices by exploring the sinusoidally coupled pendulum. Loss of stability of the breather solution is studied. We also find the existence of discrete breather in lattices with parameter mismatches. Breather phase synchronization is exhibited for the coupled chaotic oscillators.

The Wigner band random matrix model is studied by making use of a generalization of Brillouin-Wigner perturbation theory. Energy eigenfunctions are shown to be divided into perturbative and nonperturbative parts. A relation between the average shape of eigenstates and that of the so-called local spectral density of states (LDOS) is derived by making use of some properties of energy eigenfunctions drawn from numerical results. Several perturbation strengths predicted by the perturbation theory are found to play important roles in the variation of the shape of the LDOS with perturbation strength.

A scaling property about the parameter shifts for the critical points of the period-doubling bifurcation is exploited for the non-stationary dynamical systems.

We show that by virtue of the <λ| representation (Hong-Yi Fan, Phys. Lett. A 126 (1987) 150) the Landau wavefunctions of an electron in a uniform magnetic field can be immediately derived without solving the corresponding Schrödinger equation. It turns out that the differential operation form of the electron's dynamic Hamiltonian, adopted in standard quantum mechanics textbooks, is actually expressed in <λ| representation.

By the method of φ-mapping topological current theory, the bifurcation behavior of the topological current is discussed in detail in the O(n) symmetrical time-dependent Ginzburg-Landau model at the critical points of the order parameter field. The different directions of the branch curves at the critical point have been obtained.

The multi-order exact solutions of the two-dimensional complex Ginzburg-Landau equation are obtained by making use of the wave-packet theory. In these solutions, the zeroth-order exact solution is a plane wave, the first-order exact solutions are shock waves for the amplitude and spiral waves both between the amplitude and the shift of phase and between the shift of phase and the distance.

We study the properties of heavy fermions in the vector-like representation of the electroweak gauge group SU(2)_W×U(1)_Y with Yukawa couplings to the standard model Higgs boson. Applying the renormalization group analysis, we discuss the effects of heavy fermions to the vacuum stability bound and the triviality bound on the mass of the Higgs boson. We also discuss the interesting possibility that the Higgs particle is composed of the top quark and heavy fermions. The bound on the composite Higgs mass is estimated using the method of Bardeen, Hill and Lindner (Phys. Rev. D 41 (1990) 1647), 150 GeV ≤ m_H ≤ 450 GeV.

We derive a free boson representation of the Yangian double DY_ħ(sl_N) with arbitrary level k by the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents cannot be obtained in the same way. From this point of view, the Yangian double with centre cannot be regarded as the degenerated case of the quantum affine algebra.

A simple way to explain quantum behavior of supersymmetric non-isotropic traps is proposed in the framework of semiunitary formulation of supersymmetric quantum mechanics. Using semiunitary formulation we can simultaneously supersymmetrize the complete set of observables, especially including angular moment.

The isospin dependence, recently observed in Sn + Sn reactions at 40 MeV/nucleon, is discussed within the framework of two simple nuclear multifragmentation models, namely the site percolation and the nucleation-evaporation models. It is shown that both the models are able to discriminate between ¹¹²Sn+ ¹¹²Sn and ¹²⁴Sn+ ¹²⁴Sn reactions. The nucleation-evaporation model succeeds to reproduce nicely the experimental data, but the site percolation model fails in doing that, even if the cluster noncompactive effect is taken into account. The calculations indicate that the data are originated mainly from a single source.

Semi-infinite nuclear matter has been investigated in relativistic Thomas-Fermi and Hartree approximations based on the modified derivative scalar coupling model. Our results show that the spin-orbit potential has been improved by the tensor coupling. However, the surface tension and the surface thickness become considerably small with increasing of the tensor coupling constant. The effects of the σ-meson mass on the spin-orbit potential, on the surface tension, and on the surface thickness have also been discussed.

The finite volume effect of baryons in strange hadronic matter (SHM) is studied within the framework of relativistic mean-field theory. As this effect is concerned, the saturation density of SHM turns lower, and the binding energy per baryon decreases. Its influence to the compression modulus of SHM is also discussed.