One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V_{n} at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e^{-(rn)}-1 and their initial amplitude of e^{-(rn)}-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.

The dynamic equations of the proton transport along the hydrogen bonded molecular systems have been obtained by using completely quantum-mechanical method to be based on new Hamiltonian and model we proposed. Some quantum-mechanical features of the proton-solitons have also been given in such a case. The alternate motion of two defects resulting from proton transfer occurred in the systems can be explained by the results. The results obtained show that the proton-soliton has corpuscle feature and obey classical equations of motion, while the free soliton moves in uniform velocity along the hydrogen bonded chains.

Considering a model of one photon in three separated cavities, we propose a method to create a more general three-cavity entangled state with only one photon optimal for universal quantum cloning machine.

Chaotic characteristics in the iteration of logistic map(one-dimensional discrete dynamic system) are simulated and analyzed. The circuit implementation of a kind of chaotic amplifier model is based on the chaotic characteristics that chaos is sensitively dependent on its initial conditions, and the circuit simulation result is given using simulation program with integrated circuit emphasis for personal computer (PSPICE), and is compared with linear amplifier. Advantages and disadvantages of such a model are indicated.

We provide systematic calculations about the energy levels, Einstein coefficients and oscillator strengths for electric quadrupole (E2) and magnetic quadrupole (M2) transitions between n=3 and n=2 of Ne-like systems by using the fully relativistic multi-configuration Dirac-Fock method. The oscillator strengths of the E2 transitions under Coulomb and Babshkin gauges are compared with each other and show the differences from 1.2 to 12 percent. We also found that the M2 line (0.37429 nm) with the biggest oscillator strengths in Ne-like Ag^{37+} mixes with the line (2p^{5}_{3/2}3s_{1/2}3d_{5/2})_{3/2}→gs (0.37427 nm) emitted by the Na-like Ag^{36+}.

The nonlinear quantum vibrational energy spectra of amide-I in the molecular crystals acetanilide are calculated by using the discrete nonlinear Schr?dinger equation appropriate to this kind of crystals.The numerical results obtained by this method are in good agreement with the experimental values. Meanwhile, the energy levels at high excited states have also been obtained for the acetanilide, which is helpful in researching the Raman scattering and infrared absorption properties of the this kind of crystals.

The high resolution Fourier transform spectra of AsH_{3} in the region of 9720-9900 cm^{-1}, which had been recorded at a resolution of 0.015 cm^{-1}, were assigned to the (500; A_{1}) and (500; E) local mode overtones and rotationally analyzed. The effective spectroscopic parameters were obtained by nonlinear least-squares fitting the vibration-rotational Hamiltonian with the rotational energy levels up to J=6 (98 levels in all) included. The evolution of the rotational energy patterns from v=1 to v=6 shows that the tendency of normal mode to local mode vibration evolution has been stopped by perturbations in relatively high energy region.

Within the generalized definition of ABCDGH matrices, the conventional ABCDGH diffraction integral is extended for a misaligned complex paraxial system with a curved optical axis. On this basis the transformation law for Gaussian-Schell model beams through an ABCDGH systems is derived, the propagation behavior of the mutual coherence function through ABCDGH systems in the presence of random media is investigated as well.

Inversionless gain in a degenerate three-level system driven by a strong external field and by collisions with a buffer gas is investigated. The mechanism of population distribution in upper laser level, contributed by the collision transfer, as well as by relaxation, induced by pressure of a buffer gas, is discussed in detail. Explicit formulae for analysis of optimal conditions are derived. The idea developed here for the incoherent pump could be generalized to other systems.

The Hamiltonian of the process of cascaded second harmonic generation is found from Maxwell equations. In the double-gap model and under rotating-wave and effective-mass approximations, it is quantized and the generalized quantum nonlinear Shr?dinger equation (GQNSE) is obtained. Tri-photon and quadri-photon bound states are found based on general solutions of GQNSE solved via Bethe's Ansatz method. Quantum parametric gap soliton (QPGS) solution is constructed consequently, and the existence of the double-gap QPGS is predicted for the first time.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

The method of few-body physics is applied to the calculation of the low-lying states of the exciton of a GaAs disk-like quantum dot with a parabolic potential. The binding energy of the exciton in quantum disks is calculated for two different thicknesses as a function of the disk size. The four lowest exciton states dependent on the disk thickness are investigated.

Using C programming language, we have simulated the flux creep process in nonideal type-Ⅱ superconductors. Global and local magnetization curves are calculated and the logarithmic time dependence of local magnetic induction B under a constant external field is examined. The effects of nonuniform pinning potential and self-organized criticality (SOC) model on the simulations are discussed. The results show that the main feature of flux creep is the relaxation effect. The form of hysteresis loops is dependent on the magnetic field sweep rate. SOC can account for the occurrence of fluctuation to a certain extent and nonuniform pinning potential can enhance the fluctuation.

Six Q^{-1} peaks in freshly-worked PbNb_{2}O_{6} ceramics are observed by low-frequency internal friction measurement so far as we know for the first time. P_{1}, P_{2}, and P_{4} appear at the first heating process with remarkable shear modulus anomalies. But they are not observed during the cooling process or in the well-annealed samples. Those peaks are considered to be related with the working processes. P_{3} is a widened Debye relaxation peak in nature. The activation energy and pre-exponential factor are about 1.01 eV and 2.5×10^{-12} s, respectively. This peak is attributed to the interaction of domain walls and oxygen vacancies. P_{6} is corresponded with the paraelectric and ferroelectric phase transition. P_{5}, appearing near T_{c}, is thought to be caused by the viscous movement of the domain walls.

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