For many classical systems which disobey Helmholtz conditions and thus possess no stan-dard Lagrangian formulation on velocity phase space TQ, ordinary quantization procedures cannot be directly applied. By shifting to an enlarged space TTQ and viewing the systems as typically constrained ones, we propose a quantization method which seems to be practicable as illustrated by the examples.

In thls paper the method of multiple scales, theory of normal form and universal unfolding and the Melnikov's method are used to further study local bifurcations, degenerate bifurcations of codimension two and global bifurcations. Some significant results are obtained.

We have proved experimentally that the frequency shift formula of AC Zeeman effect presented by us is correct. In a ^{87}Rb atomic frequency standard we add a new microwave field which causes the frequency shift of O-O transition frequency of ^{87}Rb atomic ground state. This frequency shift as a function of frequency and power of the added microwave field is measured. The experimental results agree with theory.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

A molecular-dynamics scheme in the embedded-atom method is shown to be the efficient and accurate in studying liquid aluminium system. The ability of the method in studying liquid system is demonstrated by calculating the intent heat, self-diffusion coefficient, pair distribution function of aluminium, and so on. All of the results agree well with experimental results. The background electron density is also calculated using this method, and the result shows that a discontinuous change occurs at melting point for the electron density in the system.

By applying the dielectric continuum model, optical-phonon modes of the lattice vibration and a complete interaction Frohlich-like Harniltonian between an electron and the optical phonons including the interface phonons, the confined LO phonons and the half-space LO phonons are derived for a general coupled quantum well (GCQW) structure of polar crystals. The dispersion curves of the interface modes and the electron-interface-phonon coupling function as functions of coordinate z and wavenumber k are given and discussed for a GCQW. We find that there are eight (not ten) frequency solutions for the interface optical-phonon modes in GCQW and that, in the long-wavelength limit, the longitudinal and transverse modes in the two side materials 1 and 5 are forbidden and two new frequency solutions ω± are obtained instead. Moreover, we also find that the electron-interface-phonon coupling functions are complicated functions of k and that the phonons with long wavelengths are important and the higher-frequency modes are more important than the lower-frequency modes for the electron-phonon interaction.

High resolution electron energy loss spectroscopy, low energy electron diffraction and quadrupole maas spectrometer (QMS) have been employed to study the effect of atomic hydrogen on the acetylene-saturated pre-adsorbed Si(100)(2×1) surface and the surface phase transition at room temperature. It is evident that the atomic hydrogen has a strong effect on the adsorbed C_{2}H_{2} and the underlying surface structure of Si. The experimental results show that CH and CH_{2} radicals co-exist on the Si surface after the dosing of atomic hydrogen; meanwhile, the surface structure changes from Si(100)(2×1) to a dominant of (1×1). These results indicate that the atomic hydrogen can open C=C double bonds and change them into C-C single bonds, transfer the adsorbed C_{2}H_{2} to C_{2}H_{x}(x = 3,4) and break the underlying Si-Si dimer, but it cannot break the C-C bond intensively. The QMS results show that some C_{4} species axe formed during the dosing of atomic hydrogen. It may be the result of atomic hydrogen abstraction from C_{2}H_{x} which leads to carbon catenation between two adjacent C-C directs. The C_{4} species formed are stable on Si(100) surfaces up to 1100 K, and can be regarded as the potential host of diamond nucleation.

Photo-luminescence and electro-luminescence from step-graded index SiGe/Si quantum well grown by molecular beam epitaxy is reported. The SiGe/Si step-graded index quantum well structure is beneficial to the enhancing of electro-luminescence. The optical and electrical properties of this structure are discussed.

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

Radiative transition in δ-doped GaAs superlattices with and without Al_{0.1}Ga_{0.9}As barriers is investigated by using photoluminescence at low temperatures. The experimental results show that the transition mechanism of δ-doped superlattices is very different from that of ordinary superlattices. Emission intensity of the transition from the electron first excited state to hole states is obviously stronger than that from the electron ground state to hole states due to larger overlap integral between wavefunctions of electrons in the first excited state and hole states. Based on the effective mass theory we have calculated the self-consistent potentials, optical transition matrix elements and photoluminescence spectra for two different samples. By using this model we can explain the main optical characteristics measured. Moreover, after taking into account the bandgap renormalization energy, good agreement between experiment and theory is obtained.

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