By virtue of the technique of integration within an ordered product of operators we derive the concise normally ordered expansion of even-power of radial coordinate operator via the equation r = ∫d³x|x > < x|r, where |x > is the three-dimensional coordinate eigenvector, and r = (x² + y² + z²)^1/2. The applications to perturbation theory is briefly discussed.

The current of molecular motor model disturbed by random potentials, which involve the dichotomous and Ornstein-Uhlenbeck potential, is studied by using a finite-space correlation function. It is found that: (i) The amplitude and the correlation length of random potentials play opposing roles in the transport of the molecular motors model. (ii) a random potential with small amplitude and large correlation length is very useful in the molecular motor system.

The average transient lifetime of a chaotic transient versus the Lyapunov dimension of a chaotic saddle is studied for high-dimensional nonlinear dynamical systems. Typically the average lifetime depends upon not only the system parameter but also the Lyapunov dimension of the chaotic saddle. The numerical example uses the delayed feedback differential equation.

We have obtained two general unstable periodic solutions near the homoclinic orbits of two coupled Duffing oscillators with weak periodic perturbations by using the direct perturbation technique. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the phase portraits in the (x,u) and (y,v) planes are identical and are synchronized when the parameters of the two coupled oscillators are identical, but they are different and asynchronized when there is any difference between these parameters. It has been shown that the system parameters play a very important role in chaos control and synchronization.

We introduce an approach to expand gauge-invariant Wilson operators on the lattice. This approach is based on the non-Abelian Stokes theorem and overcomes disadvantages of the Luscher-Weisz method. It is also suitable for expanding any Wilson operator.

The asymptotic normalization coefficients (ANCs) for three bound states of ¹³C (¹²C+n) are extracted from the angular distributions of ¹²C(d,p) reactions at E_lab = 11.8MeV. With these ANCs, the calculated root-mean-square (rms) radii of these three states agree with our previous results. The ANCs are 1.93±0.17, 1.84±0.16, and 0.149±0.012fm^-1/2, and the rms radii < r² >^1/2 are 3.39±0.31, 5.04±0.75 and 3.68±0.40 fm for the ground state, the first and third excitation states, respectively. Further analyses show that the first excitation state with D₁ = 50.3% is a true neutron halo state, while the third excitation state with D₁ = 25.2% is a neutron skin state.

The mass of ⁴⁰Ti has been determined by using the isobaric multiplet mass equation method. The experimental data of ⁴⁰Ti β-decay were used to determine the level of the isospin analog state of ⁴⁰Sc. The ground-state mass excess and the Q_EC value for ⁴⁰Ti were determined to be -9060±12keV and 11466±13keV, respectively.

A general expression for the wavefunction of the scattering state of two particles is given when the direction of their relative momentum is arbitrary. The two-proton correlation function at small relative momentum is obtained with the expression when the distribution probability of the proton source is spherically Gaussian.

The Monte Carlo program built on the double giant dipole resonance model proposed by Mouze et al. [ Nuovo Cimento A 110(1997)1097] was employed to calculate the energy spectrum of alpha particles emitted in the spontaneous ternary fission of ²⁵²Cf. It has been found that in the case of the zero orbital angular momentum of alpha particles in the alpha decay of the fragments, the measured alpha spectrum can be reproduced approximately by the model without any adjustable parameter.

We have realized a cesium atomic fountain using a novel launching method. We obtained 10⁸ atoms in the magneto-optical trap experiment and studied the temperature and launching height with different frequency detuning of the lasers to cesium resonance line. A fountain with a height of 1.8cm, temperature of 30±10μK was achieved. In comparison with other experiments, we have also discussed the advantage and disadvantage of our method used in the present experiment.

The K-shell ionization cross sections of Cr, Ni and Cu elements by 7.5-25 keV electron impact have been measured. The experimental data have also been compared with the theoretical predictions of the Hippler and Mayol-Salvat models. In general, it seems that the Mayol-Salvat model can provide a better description to our experimental data.

Atomic evolutions in a single atom laser system are studied for different preparations of the initial atomic state and cavity field. Both the analytical and the numerical results are in very good agreement with the experiment carried out by Brune et al. [Phys. Rev. Lett. 76 (1996) 1800], if we choose the same parameters as the experiment. The research justified that the spontaneous emission rates are enhanced in the high-Q cavity.

In our previous papers we have studied the production of a single hole in the photon number distribution of a field state [Phys. Lett. A 240 (1998) 277; 253 (1999) 123]. In this letter we extend the procedure for the controlled creation of arbitrary number of holes.

We propose constructing a quantum interference configuration for cold atoms in a magneto-optical trap by applying a radio frequency field, which coherently couples adjacent Zeeman sublevels, in combination with a repumping laser field. One effect of this interference is that a dip exists in the absorption of the repumping light when the radio frequency is scanned. Our prediction has been indirectly detected through the fluorescence of cold atoms in a preliminary experiment.

Atoms in the coherent superposition state prepared by a pair are used as a novel optical memory material where a single interrogation pulse will produce a new pulse pair preserving the relative amplitudes and phases of the preparing pulse pair. Such a coherent superposition state can also be specially tailored along the propagation path to generate Raman scattering in a relatively short distance with very high efficiency.

Nonlinear absorption in a novel metallophthalocynine compound
(C₁₂H₂₅O)₈PcPb was investigated by Z-scan technique with the irradiation of 8 ns laser pulses at the wavelength of 532 nm. The large optical limiting response was observed. The nonlinear absorption cross section was obtained by the simulation with a simplified rate equation model in which excited triplet-triplet states absorption is dominant. The excited-state absorption cross section and its effective ratio to the ground-state absorption cross section are larger than those of C₆₀. The attenuation factor for (C₁₂H₂₅O)₈PcPb is 2.5 times larger than that of C₆₀, which is induced by the heavy atom lead interposition.

The transient transport of photo-generated carriers and temporal variation of the built-in field, during triggering in semi-insulating GaAs photoconductive switches, have been investigated by using a special Monte Carlo particle simulator. It shows that the built-in field can exceed the intrinsic avalanche field of semi-insulating GaAs under certain optical and electrical condition. In such a case, local breakdown ionization is considered to be responsible for the transition in GaAs high-gain switching. The optical and electrical triggering thresholds are calculated and the calculated values of optical and electrical thresholds and partial delay time are in agreement with the published experimental data.

We have deposited W/Si multilayer mirrors using magnetron
sputtering, and measured their reflectivity at the Beijing synchrotron Radiation Facility. The W/Si multilayer mirrors show the peak reflectivity of approximately 10% at a photo-energy of 1200eV and 10.5% at a photo-energy of 700eV at the incidence angle of 81°. So far, no higher reflectivity than that given in this letter has been reported.

A new expression of the dispersion equation of the Lamb wave in an adhesive two-layered plate is presented. The bond rigidity of the adhesive plate is accounted for in terms of a spring model. The influence of the variations of the compliance constants of the spring on the dispersion feature of Lamb modes is numerically studied. The numerical results indicate that the deterioration of the bond rigidity may cause the phase velocity decrease and the frequency-shift for a given Lamb mode, thus having a possibility for the evaluation of the bonding state of the adhesive plate by using ultrasonic wave velocity measurement. The phase-tracing method is used to measure the phase velocities experimentally and the results for an adhesive plate of aluminum-aluminum are given to verify the theoretical predictions.

Lower hybrid waves (LHWs) with a selected n_|| spectrum have been used to control the energy deposition profiles, and then the wave driven current profiles effectively in tokamak discharges. In our lower hybrid current drive experiment in HT-7 tokamak, it was found that the setup of the wave energy deposition profile is a graduation process. In the beginning phase of the wave injection duration, the waves (with different n_|| spectrum) deposit their energy almost all in the central region of the plasma column, even if their n_|| are very different. Up to around one hundred milliseconds, the wave energy deposition profiles just can take their corresponding shapes according to the n_|| spectrum of LHWs. It also shown that this evolution process is affected obviously by the LHW driven current profile, which has been formed early.

By starting with Maxwell theory of the x-ray laser propagation in collisionless plasmas, we study the phase difference of the probe beam and reference beam of x-ray laser interferometry in measuring the plasma electron density. The basic idea is to reduce the Maxwell equation to a Schroedinger-like equation. By using the quantum mechanical technique and introducing a novel picture, we obtain a modified relation between the phase and the electron density, where the phase corresponds to the interference of probe and reference light and the contribution of gradient of the electron density has been taken into account.

The bubble radius at the early stage of discharge in water is investigated using high-speed photography. Some simulation results on the bubble radius are presented, which are in agreement with the experiment results, with a maximum difference of about 10%. The reasons why the peak pressure of the first shock wave is only related to the energy released in the bubble during the first half period are addressed. The energy released in the bubble after the first half period increases the bubble pulsation period, but it produces no more than 10% under the peak pressure of the second shock wave.

Ab initio molecular dynamics simulations are performed on small single wall nanotubes. By structural relaxation, the equilibrium C-C bond lengths and bond angles are determined. Our result shows that for both zigzag and armchair nanotubes there are two nonequivalent bond lengths. One bond stretches from that of graphene sheet, while the other shrinks. Small variations on bond angles are also shown. Energy bands are calculated for the optimized structures. It is found that the intrinsic curvature of the very small nanotube greatly modifies the energy band which can no longer be well described in the tight-binding zone-folding picture. In our calculation very small nanotubes are metallic. The energy per atom fits quite well with the relation of E(R) = E₀ + f/R² even for the extreme small radius. The implications of the results on the properties of small nanotubes are discussed.

Garnet growth in the early stage of trachybasalt-eclogite transformation was observed at 2.0GPa and temperature of 860°C, 940°C and 1020°C for annealing times of 0.66-13.6h. The grain size was determined optically to be increased with increasing annealing time. The growth rate decreased with increasing grain size. The garnet growth law was: G^2.46 = 5.65 x 10^-15 t exp[-27.40 x 10³/RT], where G represents the average grain size after annealing time t, R is gas constant and T is absolute temperature.

The order-disorder phase transitions in fcc thin films are investigated by using the mean field method. The result shows that there is significant difference in the phase transitions and surface segregation between the films of even-number and odd-number layers. There are various types of phase transitions involving several ordered phases with spatial variation for the film of even-number layers, while there is only one phase transition for the film of odd-number layers.

The epitaxial growth of high-quality silicon layer on double-layer porous silicon by ultra-high vacuum/chemical vapour deposition has been reported. The two-step anodization process results in a double-layer porous silicon structure with a different porosity. This double-layer porous silicon structure and an extended low-temperature annealing in a vacuum system was found to be helpful in subsequent silicon epitaxial growth. X-ray diffraction, cross-sectional transmission electron microscopy and spreading resistance testing were used in this work to study the properties of epitaxial silicon layers grown on the double-layer porous silicon. The results show that the epitaxial silicon layer is of good crystallinity and the same orientation with the silicon substrate and the porous silicon layer.

We report a self-consistent full-potential linear muffin tin orbital band-structure calculation for heavy fermion (HF) compound LiV₂O₄. It is found that a stable local spin density approximation solution for LiV₂O₄ is lower in total energy than local density approximation calculation. We speculate that the mechanism responsible for HF properties in LiV₂O₄ might be of spin fluctuation type and is different from the Kondo mechanism in conventional 4f and 5f HF compounds.

The n-type conductive BaNb_0.3Ti_0.7O₃ thin films were grown on SrTiO₃(001) substrates by computer-controlled laser molecular beam epitaxy. The BaNb_0.3Ti_0.7O₃ films with (001) orientation are epitaxially grown on SrTiO₃ substrates, as confirmed by x-ray diffraction techniques. The root-mean-square surface roughness of the deposited thin films is measured to be 0.24nm by atomic force microscopy. The resistivity, carrier concentration and mobility of the BaNb_0.3Ti_0.7O₃ thin film are 5.9 x 10^-4Ω.cm, 1.8 x 10²¹cm^-3 and 10.7cm².V^-1.s^-1 at room temperature, respectively, which are the best values in Nb-doped BaTiO₃ thin films reported so far to our knowledge.

The transfer matrices, which transfer the amplitudes of the electric field of second- and third-harmonic waves from one side of the interface to the other, are defined for layers joined coherently, and the total transfer matrices for several sequential interfaces can be simply obtained by multiplication of the matrices. Using transfer matrix method, the interacting processes of second- and third-harmonic waves in a one-dimensional finite Fibonacci dielectric superlattice are investigated. Applying the numerical procedure described in this letter, the dependence of the second- and third-harmonic field on sample thickness is obtained. The numerical results agree with the quasi-phase-matching theory.

ZnO/TiO₂ nanocomposite films on quartz substrates were prepared by the sol-gel method, and the corresponding optical absorption properties were investigated. In the ultraviolet region, it was found that the position of fundamental absorption edge partially depends on the composition of the ZnO/TiO₂ films, and shifts toward a shorter wavelength with the increasing content of ZnO in the films. Moreover, a blueshift of the absorption edge resulted from a quantum size effect and the quantum confinement effect was observed in the ZnO/TiO₂ system.

We have numerically analyse the stability of sonoluminescing bubbles in a relatively wide range of experimental parameters and have determined the stable domains for single-bubble sonoluminescence in the P_a-R₀ phase diagrams. We map the phase diagrams when the frequency of the driving pressure f is 26.5kHz at the ambient pressure P₀ of 2 and 0.5atm, and the frequencies 10 and 1kHz at 1 atm. When the frequency is lowered to 1kHz, the ambient radius R₀ can be as large as 20μm.

ZnO nanorods with different morphologies were fabricated through a simple reaction method. They were characterized by means of powder x-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM) and energy-dispersive x-ray (EDX) spectroscopy. FE-SEM images showed that the shapes of the ZnO nanorods including straight nanorods, spear-like nanorods with sawtooth-shaped surfaces and lotus root-like nanorods. XRD and EDX indicated that all the nanorods are composed of hexagonal ZnO.

A thermodynamic theory about the dependence of morphology of SiO_x nanowires on the super-saturation of alloy liquid droplets has been proposed on the basis of the vapor-liquid-solid growth mechanism and has been supported experimentally. By changing the Si-concentration in the Au-Si liquid droplets formed on the Au-coated Si substrate, firework-, tulip-, and bud-shaped SiO_x nanowires were synthesized by a thermal evaporation method and distributed concentrically around some void defects in the Si substrate. The voids were formed underneath the surface of the Si substrate during the thermal evaporation at 850°C and resulted in the Si-concentration deficient thus different saturation of Au-Si droplets. Electron microscopy analysis showed that the nanowires had an amorphous structure and were terminated by Au-Si particles.

We present an alternative scheme exactly to implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a traveling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.

A model considered gas outflows due to supernova explosions is developed for the star formation and chemical enrichment for the globular clusters(GCs) in the Milky Way Galaxy. Through Monte-Carlo simulations, the observed global properties of GCs can be well reproduced, including the metallicity distribution, no-correlation between cluster masses and galactocentric distances, etc. The predicted mass function of the parent clouds for the observed GCs at present-day can be well described as a power law with the index of -1.8, which is consistent with the current observations for the molecular clouds.

It is shown that the power spectrum defined in the Synchronous gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of Universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge.