The effect of coupled-mode-LO phonons on the electronic transport in a polar semiconductor is studied within a model which takes the internal thermalization time of the LO phonon system and the relaxation time of the whole lattice as parameters. Our analysis shows that although the hot-electron energy-loss to LO phonons is drastically enhanced and the LO-phonon-induced linear mobility is markedly reduced by the formation of coupled modes at low temperatures, in a realistic polar semiconductor when all the scattering mechanisms included, the coupled-mode effect on the transport properties is almost buried.

All the previous homogeneous theories result in M_ΧΧ = 0 which are at variance with the experimental data. It is for this reason, previous theories have consistently used experimental value of M_ΧΧ in calculating thermopower tensor S. The inhomogeneous and non-equilibrium formalism proposed by Dyakin et al. was generalized to including both transverse and longitudinal modes of electron-phonon interaction and considering the broadening of the Landau level. The resulting formula gives theoretical values of M_ΧΧ for GaAs/AlGaAs heterojunctions which are in accord with experimental ,data at oscillation phases but (λ_p/)^l/2 times smaller than experimental data for T = 1.275 K, 2.937 K, 5.005 K and C = 0.20 where λ_p and are the phonon mean free path and effective thickness of the heterojunctions. By means of the semi-empirical formula of MzZ with extra factor (λ_p/)^l/2 in, phonon drag magnetothermopower can be calculated from theoretical values of M_yΧ and M_ΧΧ.

Using the Abrikosov's pseudo-fermion representation of a single spin S and the Larsen's note with pseudefermion energy λ = 0, we describe a procedure which allows calculation of spin-spin interaction as well ts spin-electron (hole) interaction for the case of spin S = 1 by usingstandard methods including the linked cluster theorem of diagrammatic perturbation theory. In particular we derive the multiple-exchange-mediated interaction in the case of S = 1 and predict the possibility of a higher Tc such as 170 K.

We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormaliza tion group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface. specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large and om field.

The collective magnetoplasmon polariton excitations in a semiconductor superlattice with the thicknesses arranged in Thue-Morse sequence are studied. We take the effect of retardation into account and assume the system is subjected to an external static magnetic field applied parallel to the interfaces. It is found that the spectrum of the polariton has the Cantor-like structure, and the total widths of the bands show scaling properties with increasing the generation. The external magnetic field makes the bands become more narrow and shift to higher frequencies for the optical modes and to lower frequencies for the acoustic modes. For a given excitation frequency, the localization properties,of the modes will be changed if we vary the external field.

Four methods of determining the variational parameter in the varia tional-cumulant expansion (VCE) are studied on the 2-dimensional Ising model. A comparison with the exact result shows that the main-variation method is the best one at low temperature, the completevariational method is better than others at high temperature, the accumulation-point method is the best one to approximate the intermediate coupling region, and each of the methods is analyzed from the original formulas or conjectures. Some suggestions are given in order to get optimal results. The VCE is also analyzed Gom a point of view of symmetry breaking for the first time.

The combined effect of several noises has been proposed recently. It has displayed that the presence of the correlation between noises can change the properties of the stochastic processes. In this paper, a general effective Fokker-Planck equation (FPE) with correlated noises is derived. The stationary distributions and the moments of two kinetic models under two correlated noise sources are obtained. The effects of the interference of additive and multiplicative noises are analyzed.

An improved hierarchical cascade model (PIDD model) has been obtained by using pseudoinverse method without degenerate states in the framework of the hierarchical model improved by Deshpande, the PIDD model not only avoids errors on classification of patterns, but also suits to store correlative patterns. The dynamic behavior of the PIDD model has been analyzed, and phase structure and self-consistent equations have also been obtained ,by using the replica method.

A general theory for the linear transform in Bargmann-Fock space of n-mode boson system is presented. The group structure of transform is analyzed and the explicit expressions of transform operations in terms of normal ordering are given. As applications, a series of useful iden tities are given, the decoupling problem for general two-boson interaction and the normal product calculation of boson exponential quadratic operators are studied.

For a type of nonlinear Schrodinger equations, we get a set of formal series symmetries. For a special integrable bilinear Schrodinger equation in (2 + 1)-dimensional spacetime, some truncated symmetries which constitute an infinite dimensional Lie algebra are obtained.

We first give for the combined KdV-mKdV equation, an inverse strong symmetry and five symmetries, and then we constitute six sets of symmetries and a generalized hierarchy of combined KdV-mKdV from these symmetries by using strong symmetry and its inverse.

In this paper we suggest a new prescription for the Hamiltonian reduction of the SL(3, R)WZNW model by generalizing the famous BFOFW theory. As a result, a conformal system with conformal weights in 1/3 sequenceis induced. We call the system the extended W₃² Toda model because its conformal invariance is described with a nonlinear W₃²-algebra. Relying on the analyses in this paper, it seems that the Hamiltonian reduction procedure itself, for WZNW model, does not demand that the survived Kac-Moody currents should be preserved to have clear conformal dimensions.

Using the thermal coherent state approach, we investigate the finite temperature quantum double sine-Gordon (DsG) field theory. From the stability conditions of the vacuum states of effective potential, the exact soliton-like solution of the field equation and the resemblance between the DsG model andλφ⁴ model, we show that there exist two types of structure phase transitions among four structures of the (D+1)-dimensional DsG model similar to the symmetry restored phase transition of λφ⁴ model. For the first type of phase transition, the small kink-like solutions will disappear at the critical temperature while the large kinklike solutions will be changed continuously at the critical temperature. For the second type of the phase transitions, the metastable localized soliton-like solution will disappear, while the stable kink-like solution exists for all the temperatures and their exact form is also independent of the temperature being under or over the critical temperature.

A quantum mechanical treatment of Takeno model for energy transport in protein is presented and the cubic anharmonicity of the hydrogen-bonded interaction is also taken into account. Under the continuum approximation, two coupled nonlinear differential equations are obtained, and then exact and approximate solitary wave solutions are found. The ideal parameters for protein are used to show whether the soliton solutions can exist for real protein molecules.

The Glauber approximation in the laser-assisted inelastic collisions is derived in detail. The scattering S-matrix elements are successfully reduced so that the analytical expressions for S-matrix elements are obtained. An example for numerical calculation is given and the results are compared with the first Born approximation.

In a tight-binding model, we find that the equation of the Green's function in a onedimensional mesoscopic ring threaded by a Aharonov-Bohm (AB) flux can be exactly solved. From the poles of the Green's function, the eigenvalues are obtained and are periodic in the AB flux with period h/e. However, the periodicity of the persistent currents is determined by the number of electrons in the ring.

Through the calculation of the effective potential and the excited state energies for the sinh-Gordon and the sine-Gordon models in (D + 1) dimensions, we show that the variational technique of Bogoliu bov transformations is equivalent to the Gaussian wave-functional approach.

It is found that Dirac's original consistency conditions do not suffice to generate all the secondary constraints and determine all the multipliers in front of the second-class constraints for the general singular Lagrangian sys tems. Cawley 's second counter example of Dirac's conjecture just has this feature. This may lead to the fact that the equivalence of Lagrangian and Hamiltonian formalism is not guaranteed and even dynamics of Hamil tonian formalism is not completely determined. In order to overcome the above difficulties, an augmen ted algorithm for generation of constraints-the algorithm of the extended consistency conditions is proposed. In this new algorithm, Cawley's second example is no longer a counter example of Dirac's conjecture.

We derive the q-Taylor's formula with its q-remainder through the q-differentiation approach. Comparison between q-Taylor's expansion with the ordinary Taylor's formula is made, which shows that the q-remainder is different from the ordinary one.

We obtain a new class of exact analytic solutions of the BKP equation which are called chain solutions because they are analogous to the, soliton solutions of the KP equation. The rational solutions called lumps are shown to include in this class as a Special limiting situation.

In this note, we claim that we have obtained all nondegenerate solutions of Yang-Baxter equation with spectral parameter for square-lattice eight-vertex model without "zero-field" conditions by several solution transformations and six basic solutiofis with the help of Wu algorithm.

A perturbation variational approach to atomic behavior in strong laser fields is expressed briefly. For a wide range of cue = 0.1 ～ 50, the ground state energy of H atom in laser fields is obtained by the application of the perturbation variational approach. The obtained energy values agree with the previous values given by T. C. Landgraf and M. Gavrila. According to the obtained energy values, a new value of limit of validity of traditional radiation-perturbation theory (TRPT) is given.

In a cascade three-level atomic system, a parametric study of sub-Poisson or super-Poisson distribution of a stimulated field was performed. By numerical calculation and figures, we investigated the. time evolution of the sub-Poisson distribution of a radiation field. We found that different atomic initial states and different ratios of photon numb& of two radiation fields as well as different ratios of two transitions have a remarkable influence on this distribution. It is interesting to note that under certain conditions, in this cascade structure, there is a high degree of super-Poisson distribution that has not been reported in other structures. We try to explore this anomaly in detail.

Introducing the Holstein-Primakoff transformation, the coherent-state ansatz and the timedependent variation principle, we obtain two partial differential equations of motion. Employing the method of multiple scales, we reduce these equations into the envelope function equations and force the amplitude function to satisfy a nonlinear Schrödinger equation. Using the inyerse-scattering transformation, we obtain the single-, two- and N-soliton solutions and discuss the gap soliton in antiferromagnets AFeB₃.

We consider the resonant tunneling of electrons through one-dimensional Cantor-like fractal barriers. By means of a transfer matrix method, we present a general formalism to calculate the transmission and give some numerical examples. It is found that the transmission spectrum shows rich fractal patterns due to the self-similar geometry of the Cantor set. The scaling behaviour of the transmission spectrum is explored. By plotting the amplitudes of the wave functions, we also investigate the quasi-localization properties of the electrons.

We study resonant magnetotunneling in the double-barrier heterostructure in the sequential tunneling picture. The effects arising from charge buildup in the well are considered by assuming that the quasibound energy in the well varies linearly with the applied bias. Under appropriate approximations, the tunneling current density and the corresponding differential conductance are derived analytically. The results for the peak positions in differential conductance and the threshold current position are consistent with experiments.

In the weakly coupled electron-phonon systems, the existing theory pointed out that the energy spectra of polaron include four electronic bound states. Our work shows that, due to the non-nearest neighbor hopping interactions, the electron-hole symmetry of the energy band structure implied by SSH model is broken, and the numbers of the bound electronic states are changed. For a negative charged polaron, one new bound state is found near the bottom of conduction band, and the original two bound states below the bottom of the valence band and above the top of the conduction band disappear. For a positive charged polaron, five bound states have been found: one of them is an additional bound state at the top of the conduction band, the others are just the states found in the SSH model. Besides, the energy gap 2Δ is slightly shifted by turning on the long-range hopping interactions.

We give some general results concerning solutions of reflection equation associated with the Z_n symmetry Belavin model. The complete solution for the eight-vertex model is obtained.

In this article, we discuss the mean first-passage time for non-Markovian processes driven by continuous noise. Applying the iterative method to the Volterra integral equation, we obtain for the first time the series solution to the mean first-passage time problem and present the exact expression for the mean first-passage time in both the cases of rectangular distribution and long-tail distribution.

The problem of coun ting the number of periods in one-dimensional maps is extended to two discontinuous maps, the gap map and the Lorenz-like map. The numbers of periods in the gap map and the Lorenz-like map are given by 4F₂(n) and 2C₂(n), respectively, where F₂(n) and C₂ (n) are the number of periodic sequences, invariant under group C_n S₂ and C_n, respectively.

We discuss the Poisson-Lie structure of the integrable nonlinear O(3)-σ model in terms of moving local flame. The corresponding T, s matrices are given out explicitly. The fielddependent terms in r, s matrices appear to be associated with the Riemannian connection of the target manifold.

In this paper, we give the construction of thesecond constant of motion for three-dimensional classical potential systems. Correspondingly, the first- and the second-order potential equations are obtained whose solutions can directly provide the integrable systems.

In this paper, we continue the discussion for the neutron's Dirac equation and relevant problems after Ref.[1]. We consider the neutron's Dirac equation with the electric moment besides the magnetic moment, solve rigorously the neutron's Dirac equation in a uniform electromagnetic field. We also set up a relativistic neutron's spin-echo theory with a magnetic moment.

We briefly describe Brown's T-matrix formujation and deep attractive forbidden state potentials most recently proposed by Neudatchin et al. Differential cross sections of pny are calculated, and the results are in agreement with experimental data. By including the Pauli principle, Fermi momentum of target nucleus and nucleon effective mass determined by relativistic nuclear many-body theory, which reflects nucleon multiplescattering effects in nuclear medium, the hard photon productions in proton-deuteron, proton-carbon and proton-lead collisions are investigated.

In the present article the Glauber multiple scattering theory (GMST) is briefly reviewed, and a practical method of erecting the whole set of orbit diagram/matrix including the trick of compiling the computer program is proposed. It is a rather difficult problem which has never been solved before in the application of GMST. Taken as an example, the α-α collision process is calculated, and the result well fits thetexisting experimental values.

The low-lying energy spectrum of quantum Ashkin-Teller chain in the critical region is calculated by using Lanczos method. According to conformal theory, the scaling dimensions Χ and the normalizing factor ε are obtained from the energy spectrum.

The parameter imbedding method is applied to the solution of the nonlinear Schwinger-Dyson equation. A new parameter isintroduced which interpolates between a linear equation and the original nonlinear equation. We have thus an initial value problem which can be solved numerically. We present these solutions and verify that they sat&fy the nonlinear equation rather accurately.

Using the experimental values of m_b/m_r ratio to estimate the possible mass of top quark.

The linear cold-fluid theory of a free-electron laser is given where the laser field must be in the two-mode operation. The ration between the two modes of laser field is obtained. The dispersion relation is discussed in the Raman- and Compton-regimes and the space-charge wave theory is worked out.

The characteristics of FLR effects and their dependence on RF power are studied during ICRF minority heating in tokamak plasmas. With the ion energy losses being taken into consideration, a critical heating power above which FLR effects may play an important role is derived. The quasilinear Fokker-Planck equation is calculated n umericallp It is shown that the analytically derived critical power is in good agreement with the numerical calculation.