After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.

In the anomalous group velocity dispersion regime, under the influence of optical Kerr nonlinearity, the monomode optical fiber supports stable propagation of an initial soliton pulse. In this paper, we present a singular perturbation approach for the study of various perturbations acting on this initial soliton pulse, In contrast with the previous perturbation theory for this subject, this approach gets rid of dependence on any tool of the sophisticated inverse scattering transform.

For multiphoton Jaynes-Cummings(JC) model Hamiltonian, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the JC Hamiltonian, in so doing, its eigenvalues and eigenfunctions are obtained. The transition process is also calculated.

The hybrid orbitals of carbon atoms in the D_{6h<\sub> C36<\sub> molecule are studied using two rotating ellipsoid models. The model 1 is 1.66R for the short semi-axis and 2.34R for the long semi-axis, and the model 2 is 1.78R and 2.26R respectively, where R is the C-C bond length. By comparison,we think the model 2 to be more proper in revealing the electronic properties of the D6h<\sub> C36<\sub> molecule. The component of s orbitals in the π states hybridized for each of the atoms is much larger than C60<\sub>, in which the s-orbit component is 0.0380 and the p-orbit is 0.9620. The most component is 0.2098 and the least is 0.0482 for model 1; the most is 0.1764 and the least is 0.0656 for model 2.}

Numerical simulations of ionization and dissociation processes of hydrogen molecular ion H_{2}^{+} interacting with two-color intense ( 10^{14}W/cm^{2}-10^{15}W/cm^{2}) ultrashort (the duration ≈ 22fs) laser pulse are made. The result shows that the ionization and dissociation processes are strongly dependent upon the relative phase between the two color fields. It means that, in the case of ultrashort pulse, the phase coherence control of ionization and dissociation processes can be realized.

We report the tight-binding molecular dynamics simulations of C_{60<\sub> impacting on a graphite (0001) surface with different incident energy. The simulations provide detailed characterizations of the microscopic processes occurring during the collisions and show insight into the deposition mechanisms of C60<\sub> on semiconductor substrate.}

It is shown that photon-excitation state defined by |α,k〉_{q}=a^{{\dagger k}}_{q}|α〉_{q} (k=1,2,3...) up to a normalization constant can be produced in nonlinear processes in q-nonlinear cavities. The mathematical and quantum statistical properties of this state are studied in detail. We show that this state, along with the number states absented in it, forms a complete set. We also show by numerical method that this state exhibits quantum-squeezing for some values of |α| and always reveals quantum-antibunching effect.

A complete whispering-gallery-mode microsphere laser theory is developed, which combines usual laser semiclassical theory with Lorenz-Mie theory. The linear and nonlinear problems of the microsphere lasing are dealt with in the universal mode picture. The threshold condition, average amplitude of the steady state and frequency effect are obtained. A comparison between the theory and experiments is also made.

We have employed phase-diffusion model to study the effects of laser field correlation on the Raman-enhanced nondegenerate four-wave mixing (RENFWM). The different roles of the field fluctuations have been pointed out. A time-delayed method has been proposed to suppress the thermal background. An enhancement of the ratio between the resonant and nonresonant RENFWM signal intensities was found as the time delay is increased when the laser has broadband linewidth. When the lasers have Gaussian line shape, we also present a second-order coherence function theory to elucidate the temporal asymmetry behavior of the RENFWM.

We have employed second-order coherence function theory to study the nonlinear effects of third-and fifth-order on polarization beats in a four-level system (TPBFS and FPBFS). It is found that the different temporal behavior of the beat signal in TPBFS and FPBFS depends on the stochastic properties of the lasers and transverse relaxation rate of the transition. We have considered the cases that pump beams have either narrow band or broadband linewidth and found that for both cases a Doppler-free precision can be achieved in the measurement of the energy-level difference between two excited states which are dipolar forbidden from the ground state. We also discussed the spatiall modulation behavior of the beat signal.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

We develop a Frenkel-Kontorova model to analyze the microscopic origins of vacancy-line interactions in a pseudomorphic adsorbate system. The atomic positions in the ground states are obtained by use of the gradient method. Our numerical results can explain the 2×N reconstruction observed in Ga/Si(112).

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

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in the one-dimensional dimerized Hubbard model. The formation of charge and spin gaps is investigated both for the half-filled electron band and away from the half-filled band. The scaling laws of the charge and spin gaps with the dimerization parameterΔ and the repulsive interaction strength U are obtained.

The method of few-body physics is applied to treat a D^{-<\sup> center quantum dot system in a magnetic field. The magnetic field is applied in the z direction. Using this method, we investigate the energy spectra of low-lying states of D-<\sup> center quantum dots as a function of magnetic field. The dependence of the binding energies of the ground-state of the D-<\sup> center are calculated as a function of the dot radius with a few values of the magnetic field strength and compared with other results.}

Bulk superconducting La_{2}CuO_{4+δ<\sub> single crystals are obtained by using electrochemical intercalation technique from the as-grown insulating samples. Oxidation is carried out by constant current I=10μA at temperature T=70℃ and room temperature, respectively. Structure and magnetic properties are studied by low-temperature X-ray diffraction and susceptibility measurements. A superconducting phase with Tc of 19K and δ-0.12 can be attributed to the formation of oxygen clusters. Room temperature oxidation is inhomogeneous: two superconducting phases with Tc1<\sub> of 24K and Tc2<\sub> of 8K and an antiferromagnetic phase are coexisting in the crystal. It is found that the appearance of Tc in this system has the "step" tendency.}

Magnetic and transport properties of La_{0.5}Ca_{0.5}MnO_{3} have been investigated by measuring the magnetization and resistance in zero-field-cooled (ZFC) and field-cooled (FC) modes. Conspicuously irreversible behaviors of magnetization/resistance in the two different modes were observed below the charge ordering transition temperature (T_{CO}). The ZFC and FC magnetizations at 5K, as functions of the magnetic field, coincide for μ_{0}H≤1T. Afterwards, the ZFC magnetization tends to an approximate constant, but the FC one increases linearly with increasing field. There exists an excellent correspondence between magnetization and resistance below T_{CO}. All the results suggest that the ferromagnetic clusters embed in the charge-ordered matrix. The phenomenon of ferromagnetic clusters growing up easily in the FC procedure has been interpreted according to the model of thermally activated two-level system.

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