By using the method with which the trajectories of dissipative maps can be derived from the Hamiltonian, we study the symbolic dynamics of Henon map and its relation with the symbolic dynamics of unimodal map, and compute the topological entropy as a function of the parameter a and b. Finally, the boundary of the region where the topological entropy exists on the parameter plane is given.

The optical properties of two-dimensional antiferromagnetic lattice were etudied through the theoretical calculation of the high-frequency hoping conductivity in a spin-deneity-wave background. The effect of the strong spin correlation in the bag excitation region on the conductivity is diecueeed. Calculations have been made under the mean-field approximation including self-energy and vertex contributions.

We derive equations for the single and joint probability distribution of systems driven by colored Poisson noise using the ordered cumulant technique. We also derive the equation for the correlation function. We discuss an example for which the correlation function and the associated relaxation time are calculated.

The isoscalar giant monopole and quadrupole states in finite nuclei are studied in a relativistic δ-ω model by making use of a local Lorentz boost and scaling method, and the nuclear surface and the density distribution are treated in the relativistic Thomas-Fekmi approximation.The excitation energies of the giant resonances are self-consistently calculated. It is found that the excitation energies of giant monopole arehbasically in agreement with experimental data for all nuclei and those of giant quadrupole for light nuclei. Coupling constants and δ-meson mass in the theory are chosen to fit static properties of nuclear matter.

In this paper a systematic method, based on Jimbo's theorem, for constructing the spectrumdependent trigonometric solutions, as well aa the rational ones, to the Yang-Baxter equation is presented. Some solutions obtained by this method are discussed. The link polynomials constructed from the trigonometric solutions are obtained.

We discuss the relations between the K-M matrix and the masses of the quarks and leptons in the case of four generations, and give the exact expression of the K-M matrix in terms of the masses of quarks and leptons. The requirement that the theoretical and experimental values of the K-M ,matrix are consistent leads to an allowed range of quark masses of the fourth generation m_t'～400-1000 GeV, m_b'～50-130 GeV. In the leptonic sector.in comparison I with the neutrino oscillation experiments and supernova it seems that neutrino masses must have hierarchy as charged leptons.

We consider a system, consisting of a metric tensor g_μv, a scalar field Φ, a Weyl's gauge field A_μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g_μv = Φ_-2η_μv is considered in a gauge-independent manner. We point out that in a correct treatment where g_μv is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field.

The path integral method is a useful tool which can be used to calculate contribution of ghost field to Casimir effect^[6]. But only free field was considered rather than interaction field. In this paper, we consider contribution of the vacuum fluctuation of QED to Casimir effect with the aid of source-field separation and Wick's expansion, and a little additional attractive force can be obtained from this method.

With quantum mechanical method, we discuss the metastable states of the quantum universe, and give two eigenstates corresponding to nonzero and zero conjugate momenta P_Φ under the assumption of p=-5, where p is the ordering factor. Analyaea for their classical evolution are made, and there comes a conclusion: The mom-entum of the scalar field of quantum state has very little effect on its later classical evolution. This gives a favourable support to the classical theory of inflation.

The behavior of the antiferromagnetic spin 112 Heisenberg Toda chain is investigated in a space of interactions which include exchange anisotropy, bond alternation and Toda-like spinlattice coupling by means of coherent-state for spin. We analyse magnetically driven lattice instabilities and find that multiphase structure only occurs under the condition, of bond alternation. Three phase diagrams and tricritical points are obtained and some relevant physical properties are discussed.

Ground state energies for shallow states of donor impurities at certain idealized defective isotropic semiconductor surfaces are calculated variationally for GaAa surfaces with electrons confined within the semiconductor. Calculations show that impurity states with donor ions located at parts projecting out of surfaces have lower ground state energiea than those with ions located at parts sunk into surfaces.

The eigenstates of an electron in two cases of one-dimensional (ID) aperiodic lattices are investigated analytically in the tight-binding approximation. The two cases of aperiodic lattices investigated are 1D Thue-Morse (TM) lattice and ID hierarchical system, both of which are non-quasiperiodic. It is shown that both the aperiodic models possess extended states. In particular, in 1D hierarchical system, there exists a finite fraction of periodic states independent of the hierarchical parameter R.

The proposal, synthesis of dense hydrogen using Hp molecules in different electronic states, is partly supported by the potential energy calculations and the rate equation analy&. Using a simple model of the screened hydrogen molecules,. the reduction of metallization pressure arising from the electron-hole pair is estimated for solid hydrogen. The result is more reasonable and in agreement with Rose comments.

A semi-analytic theory of (N, 2N) reactions incorporating central, tensor, spin-orbit and quadratic spin-orbit components of the two-nucleon t-matrix is developed. Simplifications arise pom a suitable choice of scattering geometry and an asymmetric mode of energy sharing. Using modified plane waves for the continuum wave functions results in analytic expreasions for the volume integrals.

We have calculated a minisupempace wave function for d=11 supergravity .where the 4-index anti-symmetric tensor field supplies the energy-momentum tensor. The Hartle-Hawking prdposal for the boundary conditions of the universe is also extended to the eleven-dimensional spacetime.

We argue that strong CP phase should be shifted to b and t quark masses due to the requirement of vacuum stability. The strong CP problem in low energy sector thus disappears. We predict large CP violation in electric dipole moment of W and heavy quarks.

The infinite-dimensional indecomposable representations are constructed by using the purely algebraic method and the matrix elements for these representations are obtained in an explicit form. Each familiar finite-dimensional irreducible representation ia induced on a quotient space.

Recently, Hong FU, H: Haken and A. Wunderlin proved the convergence of the slaving principle in a simplified model: the Haken model (HM)^[1]. In the present study, by virtue of introducing an auxiliary series of positive terms corresponding to the formal slaving series of variable terms and solving the nonlinear differential equation for the zero order faat variable so(t), we succeeded in generalizing the Hong FU's method to several typical models.

The thermal conductivity of periodic composite media with spherical inclusions embedded in a homogeneous matrix is discussed. Using Green's function, we show that the Rayleigh identity can be generalized to deal with the thermal properties of these systems. A technique for calculating effective thermal conductivities is proposed. Systems with cubic symmetries (including simple cubic, body centered cubic and face centered cubic symmetry) are investigpted in detail, and useful formulae for evaluating effective thermal conductivities are derived.

The RVB model is investigated by a mean field theory, in which the holon is expressed by a fermion operator, and the spinon by a boson operator. The effective holon-holon interaction by exchanging the spinons is derived for T≠0. It is found that the interaction is attractive.

The superconductivity window of the Cu-containing high T_c superconductors is studied. It is found that in the case of doping carriers the chemical potential is nonzero and depends on the concentration of carriers δ, which inevitably introduces an upper limit of δ for T_c. The discussion is started with a two-band model Hamiltonian, and the superexchange interactions between 0-0 holes are analyzed by the canonical perturbation theory. Some conclusions are drawn finally.

By means of kneading theory the gap map is studied based on the admissibility conditions.A criterion for the existence of chaos is derived. The structure of the skeleton is analyzed by using two transformations for symbols. The boundary of chaos for the gap map is described.

We successfully applied the Green function theory in GW approximation to calculate the quasiparticle energies for semiconductors Si and GaAs. Ab initio pseudopotential method was adopted to generate basis wavefunctions and charge densities for calculating dielectric matrix elements and electron self-energies. To evaluate dynamical effects of screened interaction, GPP model was utilized to'extend dieletric matrix elements from static results to finite frequencies. We give a full account of the theoretical background and the technical details for the first principle pseudopotential calculations of quasiparticle energies in semiconductors and insulators. Careful analyses are given for the effective and accurate evaluations of dielectric matrix elements and quasiparticle self-energies by using the symmetry properties of basis wavefunctions and eigenenergies. Good agreements between the calculated excitation energies and fundamental energy gaps and the experimental band structures were achieved.

The liquid-gas phase transitions in nuclear matters are investigated by employing the thermal Fermi-gas model and the Skyrme-type nucleon-nucleon interactions. Various situations with different sophistications are under consideration. The nuclear equations of state (EOS), P(p_cT) or µ(p_cT), are derived for these situations. From these EOS, the critical temperature T_c and density p_c are obtained by making use of the inflection conditions.

Employing the closed-time-path Green's function formalism (CTPGF), the electron selfenergy and vertex function at finite temperature are derived at one-loop level. The so-called "double termn" does not appear in our approach and thus, the unitarity of the theory is ensured automatically. The temperature-dependent mass and vertex corrections are dispersive due to the existence of electron-positron pair background. In the nonrelativistic limit, the explicit forms of shifts due to temperature of both mass and Lande's g factor are given, and their low temperature (T<>m) limits are discussed.

In this paper the classical Fredholm theory is generalized. The conceptions of the generalized fredholm denominator (GFD) and generalized Fredholm numerator (GFN) are defined. A set of parameter imbedding equations for GFD and GFN is deduced. In this way, the eigenvalue problem of the BS equation in ladder approximation with self-energy graphs, and the eigenvalue problem of nonlinear parameter integral equation, are carried over into an initial-value problem of a set of ordinary differential equations.

By means of the renormalized Dirac spinor wave function and through. the introduction of an effective interaction operator, the exact ~ethe-saypetere quation for multi-fermion bound states has been reduced to an equivalent Pauli-Schrodinger equation. As a result, the specific form of the latter equation in the static approximation has directly been given as well. In comparison of the effective interaction operator appearing in the Pauli-Schrodinger equation with the corresponding S-matrix, a substantial difference between both interactions acting in the bound state and the scattering state emerges which is important to determine an interaction potential in the bound state.

The quantum version of the Sherrington-Kirkpatrick model in a transverse field is investigated by combining the pair approximation with the discrete path-integral representation. The free energy and the field-dependent freezing temperature T_c(Г) of the model are obtained,and the classical result for the vanishing of the transverse field (Г → 0) can be reproduced.

An explicit nonlinear superposition formula for the nonlinear Schrödinger equation is derived for the first time.

The magnetic excitation at the auiface of a substitutionally disordered antiferromagnet is etudied by using the Bethe-lattice method. Some numerical resulte are presented.

The Feynman rules are established for thermodynamic Green's functions of an electron gas by means of the closed-time-path Green's function formalism which avoids infinite sums over discrete frequencies and analytical continuations. The thermodynamic potential of the system is 0btained.h a closed form in the random phase approximation which reduces correctly at 0° K to the RPA correlation energy of the ground state theory.

A new Lax pair of the modified nonlinear Schrödinger equation is introduced in terme of the variable of the Fourier transform λ. The Lax pair has no usual symmetries between 12 and 21 elements and avoids the factor λ^1/2. The basic equation of inverse scattering transformation is deduced in the Zakharov-Shabat form as well as in the Marchenko form.

Taking into account the interaction of an electron with both bulk longitudinal-optical (LO) and interface-optical (IO) phonons, the cyclotron resonance of an interface magnetopolaron at finite temperatures is investigated by using the generalized Larsen perturbation-theory method. It is shown that the absorption and emission resonance must be considered at the same time at finite temperatures. The results also show the important role played by the electron-IO phonon interaction. For the GaAa/GaSb structure, splitting of the cyclotron resonance spectrum and temperature dependence of the threefold splitting cyclotron resonance mass of the magnetopolaron in the resonant magnetic field region are studied.

In this paper we present for the first time completely analytical variational expressions for calculating the binding energies of the low-lying bound states of a hydrogenic donor in a quantum well (QW). These expressions can be used for the problem of the binding energy of an impurity in a general manner, e.g. for calculating the binding energies of a donor associated with subband states of any order in the QW with any arbitrary potential profile. 70 demonstrate the utilization of these expressions we have theoretically studied the binding energies for the ground and a few low-lying excited etates of a hydrogenic donor in a stepped quantam well (SQW). The variations of the binding energies for these donor etates with impurity positions are investigated for different heights of the step potential. The numerical calculation results show that the binding-energy curves in the SQW, in contrast to the case of the flat quantum wells (FQW's), exhibit a non-symmetrical structure relative to the center of the QW and depend on the sub-barrier potential. The peak position in the binding energy curves shifts away from the region occupied by the sub-barrier as increasing sub-barrier height. The maximum in the binding energies increases as the step potential increaaes. These effects can be interpreted by referring to the variation of the electron probability-density distribution and of the lowest subband in the SQW. The shape of the binding-energy curves related to the 2po-like state is different from the other states. It is associated with the particular feature of the wave function of the 2po state in the QW.

Bethe-Salpeter equation in ladder approximation with self-energy graphs is diecussed for the model problem of two dftinguiahable equal-mass scalar particles exchanging a single maesive ecalar boson. The spectral features are analyzed.

By means of the finite temperature Gaussian effective potential (FTGEP) method, the (1+1) and (2+1) dimensional quantum double sine-Gordon (DsG) field theories are studied nonperturbatively for finite temperature. The explicitly FTGEP is obtained for both (1+1) and (2+1) dimensional DaG models. The temperature-dependent Coleman phase transition conditions obtained by us would reduce to the known results g_cr² when T→0. The alternative explanation of the Coleman phase transition at finite temperature is that for fixed coupling constantg² there is a critical temperature T_cr (whose value depends ong²) such that the theory becomes unstable when the temperature of the system exceeds the critical value T_cr.

We give the details of rigorous proof of some mass inequalitiee in a vector-like gauge theory based on any simple group G. These mass inequalitiee lead to the conclusions that in auch a theory the chiral symmetries associated with all G representations of quarks must be spontaneously broken, and the persistent mass condition ie justified for any composite particles when the vacuum angle is zero or massless quarks exist.

The infinite many nonlocal conserved currents are given for the principal chiral model. Wess-Zuminc-Witten chiral model and the supersymmetric chiral model with respect to the new hidden symmetry transformatione. It is shown that these conserved currents are related to the classical r-matrix and thus decompose into many families. The approach used here provides a systematic method to derive the Casimir operators for the infinite dimensional Lie algebras in its nonunitary and nonhighest weight representations.

Geometric quantization of multiparticle systems in 2 dimensions is studied. The interpretation of the global geometry to the phase factors describing the quantum statistics of the systems is presented.

The universal solution of Oppenheimer-Volkov equations with strange quark matter equation of state of the MIT bag model is calculated in a reduced form which is independent of the MIT constant B. The lower limit of the observational pulse period of pulsars (0.69 ma) is predicted by the MIT bag constant B=(146 MeV)⁴ which ia fitted to the hadronic spectrum, while the observed lower limit of pulse period of pulaara (1.56 ms) gives an astrophysical restriction on the lower limit of the MIT bag constant as B>(97 MeV)⁴.