The Lie-form invariance of a nonholonomic mechanical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechanical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is given to illustrate the application of the results.

Based on the invariance of differential equations under infinitesimal
transformations, Lie symmetry, laws of conservations, perturbation to the
symmetries and adiabatic invariants of Poincar\'{e} equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincar\'{e} equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.

Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear
differential-difference equations.

We propose a scheme for teleporting a two-atom entangled state in
cavity quantum electrodynamics (QED). In the scheme, we choose a
single Einstein--Podolsky--Rosen (EPR) pair as the quantum channel which
is shared by the sender and the receiver. By using the atom--cavity-field
interaction and introducing an additional atom, we can teleport
the two-atom entangled state successfully with a probability of 1.0.
Moreover, we show that the scheme is insensitive to cavity decay
and thermal field.

Deterministic and exact teleportation can be achieved via two partially
entangled pairs of particles [Gu Y J 2006 {\em Opt. Comm.} {\bf 259} 385]. The key point of the protocol is a generalized measurement described by a positive operator-valued measure, which can be realized by performing a unitary operation in the extended space and a conventional Von Neumann orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the teleportation. Our method for constructing quantum circuits differs from the usual methods based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.

The proposals on entanglement diversion and quantum teleportation of
entangled coherent states are presented.In these proposals, the entanglement between two coherent states,\alpha\rangle and $|-\alpha\rangle$, with the same amplitude but a phase difference
of $\pi$ is utilized as a quantum channel. The processes of the entanglement diversion and the teleportation are achieved by using the 50/50 symmetric beam splitters, the phase shifters and the photodetectors with the help of classical information.

An effective teleportation scheme for an unknown ionic internal state
via trapped ions is proposed without joint Bell-state measurement
(BSM). In the constructed quantum channel process, we make use of
entanglement swapping to avoid decrease in entanglement during
the distributing of particles. Thus our scheme provides new prospects
for quantum teleportation in a longer distance. The distinct
advantage of our scheme is insensitive to the heating of vibrational
mode. Furthermore, our scheme has no any individual optical access,
and the successful probability also can reach 1.

An elliptical Gaussian wave formalism model of a charged-particle beam is
proposed by analogy with an elliptical Gaussian light beam. In the paraxial approximation, the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains.
Therefore, the propagation and transform of charged-particle beam
passing through a first-order optical system is represented by the
\textit{ABCD}-like law.As an example of the application of this model, the relation between the beam waist and the minimum beam spot at a fixed target is discussed. The result, well matches that from conventional phase space model, and proves that the Gaussian wave formalism model is highly effective and reasonable.

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics.

This paper investigates robust unified (lag, anticipated, and complete)
synchronization of two coupled chaotic systems. By introducing the concepts
of positive definite symmetrical matrix and Riccati inequality and the
theory of robust stability, several criteria on robust synchronization are
established. Extensive numerical simulations are also used to confirm the
results.

The complex Ginzburg--Landau equation (CGLE) has been used to
describe the travelling wave behaviour in reaction--diffusion (RD)
systems. We argue that this description is valid only when the RD
system is close to the Hopf bifurcation, and is not valid when a
RD system is away from the onset. To test this, we study spirals
and anti-spirals in the chlorite-iodide-malonic acid (CIMA)
reaction and the corresponding CGLE. Numerical simulations confirm
that the CGLE can only be applied to the CIMA reaction when it is
very near the Hopf onset.

Neurons at rest can exhibit diverse firing activities
patterns in response to various external deterministic and random
stimuli, especially additional currents. In this paper, neuronal
firing patterns from bursting to spiking, induced by additional
direct and stochastic currents, are explored in rest states
corresponding to two values of the parameter $V_{\rm K}$ in the Chay
neuron system. Three cases are considered by numerical simulation
and fast/slow dynamic analysis, in which only the direct current
or the stochastic current exists, or the direct and
stochastic currents coexist. Meanwhile, several important bursting
patterns in neuronal experiments, such as the period-1
``circle/homoclinic" bursting and the integer multiple
``fold/homoclinic" bursting with one spike per burst, as well as
the transition from integer multiple bursting to period-1
``circle/homoclinic" bursting and that from stochastic
``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are
investigated in detail.

Absorption is the origin of luminescence. But it must be noticed that the
lifetime of luminescence might reversely influence the rate of
absorption. In this paper, it is reported that the luminescence intensity of copper and manganese changes with the driving frequency at constant voltage.The variation of luminescent intensity depends only on the lifetime of luminescence but not on the type of quenching or other factors. Generally the rate of absorption is dominantly determined by the material property and the lifetime of luminescence centres, the absorption of shorter lifetime centre will be larger than that of the longer lifetime centre at the same excited condition.

The field entropy can be regarded as a measurement of the degree of
entanglement between the light field and the atoms of a system which is
composed of two-level atoms initially in an entangled state interacting with the Schr\"{o}dinger cat state. The influences of the strength of light field and the phase angle between the two coherent states on the field entropy are discussed by using numerical calculations. The result shows that when the strength of light field is large enough the field entropy is not zero and the degrees of entanglement between the atoms and the three different states of the light fields are equal. When the strength of the light field is small, the degree of entanglement is maximum in a system of the two entangled atoms interacting with an odd coherent state; it is intermediate for a system of the two entangled atoms interacting with the Yurke--Stoler coherent state, and it is minimum in a system of the two entangled atoms interacting with an even coherent state.

We propose and demonstrate a simple approach to lower the thermal quenching
effect and improve the output power of Cr:LiSAF lasers, which is
accomplished by employing two laser rods. The resonator contains two laser
rods and is designed by using two ``X'' folding cavities in cascade. A tunable
laser output of $\sim $ 180\,mW has been achieved with the pump of single-striped
laser diodes. Compared with lasers using single gain rod, the laser with
dual rods shows less severe thermal effect and increases the output by more
than two times.

Imaging properties of a two-dimensional photonic crystal slab lens are
investigated through the finite-difference time-domain method. In this
paper, we consider the photonic crystal slab consisting of a square lattice
of square metallic rods immersed in a dielectric background. Through the
analysis of the equifrequency-surface contours and the field patterns of a
point source placed in the vicinity of the photonic crystal slab, we find
that a good-quality image can form at the frequencies in the second
TM-polarized photonic band. Comparing the images formed at different
frequencies, we can clearly see that an excellent-quality image is formed by
the mechanisms of simultaneous action of the self-collimation effect and the
negative-refraction effect.

The elastic scattering properties for collisions between
two ${}^7$Li atoms are investigated in the cold and ultracold regimes
separately. Based on recent theoretical
and experimental results, we present the improved hybrid potentials for
the singlet X$^1\dsum\nolimits_{\rm g}^ + $ and triplet a$^3\dsum\nolimits_{\rm u}^
+$ ground states of the Li$_2$. Our calculated values for the scattering
lengths $a$ and the effective ranges $r_\e $ are compared with previous
ones, and found them to be in good agreement. The scattering lengths
are $34.6a_0$ for the singlet state and $-27.6a_0$ for the triplet state.
Shape resonances occur in the collisions at low energies. We also calculate
the total cross sections and the energy positions of shape resonances for
both X$^1\dsum\nolimits_{\rm g}^ + $ and a$^3\dsum\nolimits_{\rm u}^ +$ states.

A fluctuating ratchet model of non-Markov process is presented to describe the processive movement of molecular motors of single-headed kinesin KIF1A,where the fluctuation perturbation to the local potential is introduced and the detailed ATPase pathway of the motor is included. The theoretical results show good quantitative agreement with the previous experimental ones.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

The edge plasma characteristics are studied by both a movable array of
Mach/Reynolds stress/Langmuir 10-probes in the boundary region and the fixed
flush probe arrays on the 4 divertor neutralization plates at the same
toroidal cross-section in the HL-2A tokamak. The dependence of the
Reynolds stress on poloidal flow in the edge plasma is analysed. The result
indicates that the sheared poloidal flow in tokamak plasma can be induced by
the radial gradient of Reynolds stress. In the divertor experiments of
HL-2A, the profiles of the electron temperature, density and floating
potential on divertor plates are measured by the flush probe arrays. The
edge electron temperature in divertor configuration is higher than that in
limiter configuration. The temperature asymmetry between outer and inner
target plates
is observed. The result of magnetic surface reconstructed from 18 Mirnov
coils signals is presented. Both the particle recycling and the impurity
flux in the bulk plasma during divertor discharges are discussed. Neutral
gas pressure in divertor chamber, measured by fast ionization gauge during
divertor discharge, is given.

In consideration of adiabatic dust charge variation, the
combined effect of the external magnetized field and the dust
temperature on head-on collision of the three-dimensional dust
acoustic solitary waves is investigated. By using the extended
Poincar\'e--Lighthill--Kuo method, the phase shifts and the
trajectories of two solitons after the collision are obtained. The
effects of the magnitude and the obliqueness of the external
magnetic field and the dust temperature on the
solitary wave collisions are discussed in detail.

We suggest a scheme of electron acceleration by use of two tightly focused ultra-short intense laser pulses at a 100TW level. Electrons obtain a preliminary acceleration with a small angular spread by the longitudinal ponderomotive force of the first pulse. They are then injected and further accelerated to hundreds of MeV by the second laser pulse.

Diamond-like carbon (DLC) films have been deposited using three different
techniques: (a) electron cyclotron resonance---plasma source ion
implantation, (b) low-pressure dielectric barrier discharge, (c)
filtered---pulsed cathodic arc discharge. The surface and mechanical properties of
these films are compared using atomic force microscope-based tests. The experimental results
show that hydrogenated DLC films are covered with soft surface layers
enriched with hydrogen and sp$^{3}$ hybridized carbon while the soft surface
layers of tetrahedral amorphous carbon (ta-C) films have graphite-like
structure. The formation of soft surface layers can be associated with the
surface diffusion and growth induced by the low-energy deposition process.
For typical CVD methods, the atomic hydrogen in the plasmas can contribute
to the formation of hydrogen and sp$^{3}$ hybridized carbon enriched
surface layers. The high-energy ion implantation causes the
rearrangement of atoms beneath the surface layer and leads to an increase in film
density. The ta-C films can be deposited using the medium energy carbon ions
in the highly-ionized plasma.

Compared with direct ablation, confined ablation provides an effective way
to obtain a large target momentum and a high coupling coefficient. By using
a transparent glass layer to cover the target surface, the coupling
coefficient is enhanced by an order of magnitude. With the increase of the gap
width between the target surface and the cover layer, the coupling
coefficient exponentially decreases. It is found that the coupling
coefficient is also related to the thickness of the cover layer.

The divertor configuration was successfully formed and the siliconization as
a wall conditioning was first achieved on HL-2A tokamak experimentally in
2004. The divertor configuration is reconstructed by the use of the CFC
code. Impurity as an important issue is investigated in the experiments with
divertor configuration and wall conditioning. Impurities dramatically
decrease after both the divertor configuration is formed and silicon is
coated on the surface of the vacuum vessel.

Ma Tian-Peng, Ruan Huai-Lin, Hu Li-Qun, Wan Bao-Nian, Gao Xiang, Zhen Xiang-Jun, Zhou Li-Wu, Sun You-Wen, Gao Wei, Chen Zhong-Yong, Lin Shi-Yao, Kong Wei

Multi-channel soft x-ray (SX) detectors are applied to generate images of
magnetohydrodynamic (MHD) oscillation on the HT-7 tokamak, and the data
from SX cameras are analysed by using the
Fourier--Bessel harmonic reconstruction method and the singular value
decomposition. The image
reconstruction of SX emissivity is obtained on the assumption of plasma
rigid rotation. One of the important phenomena in the HT-7 discharge is the
transition from the sawtooth oscillations to the MHD oscillations when the
plasma density grows higher. The MHD structure
observed in the SX tomography is featured as follows: the magnetic surface of MHD
structure is made up of the crescent-shaped ``hot core'' and the circular
``cold bubble''. The structure of the magnetic surface is relatively stable.
It rotates in the direction of the electron diamagnetic drift at a
frequency being the oscillation frequency of the MHD oscillations.

The effect of applied longitudinal magnetic field on the
self-pinched critical current in the intense electron beam diode is discussed.
The self-pinched critical current is derived and its validity is tested by
numerical simulations. The results shows that an applied longitudinal magnetic field
tends to increase the self-pinched critical current. Without the effect of
anode plasma, the maximal diode current approximately equals the
self-pinched critical current with the longitudinal magnetic field
applied; when self-pinched occurs, the diode current approaches the
self-pinched critical current.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The effect of Re segregation on the $\alpha $-Fe $\Sigma $5 [001] (010)
grain boundary (GB) is investigated by using a software called DMol and
discrete variational method (DVM). Based on the Rice--Wang model, the
calculated segregation energy and defect formation energy show that Re is a
strong cohesive enhancer. We also calculated the interatomic energy (IE) and
bond order (BO) of several atomic pairs to investigate the mechanism of the
cohesive effect of Re microscopically and locally. The results show that IEs
of atomic pairs formed by those atoms which cross the plane of GB are
strengthened due to the segregation of Re, while the BOs of the
corresponding pairs are slightly decreased. This discrepancy demonstrates
that IE which contains the Hamiltonian of interaction between atoms is a
good quantity to describe the bonding strength. The analysis suggests that
the electronic effect between atomic pair which comes directly from
Hamiltonian is the key factor. The charge density is also presented, and the
result indicates that the bonding strength between the Fe atoms on the GB is
enhanced due to the segregation of Re, which is consistent with the analysis
of IE.

We have performed molecular dynamics simulations of structural changes due
to quenching the melting interface at a Cu $\Sigma $5(310)/[001]
symmetrical tilt grain boundary. The simulation results suggest that the
grain boundary structures due to quenching are different from those due to
heating up to the same temperature. The calculated atom density profiles
show that the grain boundary structures can be significantly changed as they
are quenched to quite low temperatures.

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

Vector quantization (VQ) is an important data compression
method. The key of the encoding of VQ is to find the closest vector among
N vectors for a feature vector. Many classical linear search algorithms
take $O(N)$ steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes
$O(\sqrt N )$ steps are presented in this paper. The unitary operation of
distance computing can be performed on a number of vectors simultaneously
because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.

Photoelectron is the foundation of latent image formation, the decay process of photoelectrons is influenced by all kinds of trapping centres in silver halide. By analysing the mechanism of latent image formation it is found that electron trap, hole trap, and one kind of recombination centre where free electron and trapped hole recombine are the main trapping centres in silver halide. Different trapping centres have different influences on the photoelectron behaviour. The effects of all kinds of typical trapping centres on the decay of photoelectrons are systematically investigated by solving the photoelectron decay kinetic equations. The results are in agreement with those obtained in the microwave absorption dielectric spectrum experiment.

The improvement of the characteristics of grooved-gate MOSFETs compared to the planar devices is attributed to the corner effect of the surface
potential along the channel. In this paper we propose an analytical model of the surface potential distribution based on the solution of two-dimensional Poisson equation in cylindrical coordinates utilizing the cylinder approximation and the structure parameters such as the concave corner $\theta _0 $. The relationship between the minimum surface potential and the structure parameters is theoretically analysed. Results confirm that the bigger the concave corner, the more obvious the corner effect. The corner effect increases the threshold voltage of the grooved-gate MOSFETs, so the better is the short channel effect (SCE) immunity.

Based on the investigation of the influence of temperatures on
parameters, including polarization, electron mobility, thermal conductivity,
and conduction band discontinuity at the interface between AlGaN and GaN,
the temperature dependence of transconductance for AlGaN/GaN heterojunction
field effect transistors (HFETs) has been obtained by using a
quasi-two-dimensional approach, and the calculated results are in good
agreement with the
experimental data. The reduction in transconductance at high
temperatures is
primarily due to the decrease in electron mobility in the channel.
Calculations also demonstrate that the self-heating effect becomes serious
as environment temperature increases.

An atomic group model of the disordered binary alloy Rh$_{x}$--Pt$_{1-x}$
has been constructed to investigate surface segregation. According to the
model, we have calculated the electronic structure of the Rh$_{x}$--Pt$_{1 -
x }$alloy surface by using the recursion method when O atoms are
adsorbed on the
Rh$_{x}$--Pt$_{1-x }$(110) surface under the condition of coverage 0.5. The
calculation results indicate that the chemical adsorption of O changes
greatly the density of states near the Fermi level, and the surface
segregation exhibits a reversal behaviour. In addition, when $x<0.3$, the
surface on which O is adsorbed displays the property of Pt; whereas when
$x>0.3$ it displays the property of Rh.

A specially designed experiment is performed for investigating gate-induced
drain leakage (GIDL) current in 90nm CMOS technology using lightly-doped
drain (LDD) NMOSFET. This paper shows that the drain bias $V_{\rm D}$ has a
strong effect on GIDL current as compared with the gate bias $V_{\rm G}$ at the
same drain--gate voltage $V_{\rm DG}$. It is found that the difference between
$I_{\rm D}$ in the off-state $I_{\rm D}-V_{\rm G}$ characteristics and the
corresponding one in the off-state $I_{\rm D}-V_{\rm D}$ characteristics, which is
defined as $I_{\rm DIFF}$, versus $V_{\rm DG}$ shows a peak. The difference between
the influences of $V_{\rm D}$ and $V_{\rm G}$ on GIDL current is shown
quantitatively by $I_{\rm DIFF}$, especially in 90nm scale. The difference is
due to different hole tunnellings. Furthermore, the maximum $I_{\rm DIFF
}$($I_{\rm DIFF,MAX})$ varies linearly with $V_{\rm DG}$ in logarithmic coordinates
and also $V_{\rm DG}$ at $I_{\rm DIFF,MAX}$ with $V_{\rm F}$ which is the characteristic
voltage of $I_{\rm DIFF}$. The relations are studied and some related
expressions are given.

Nonlinear optical properties of intersubband electrons in a
3-level quantum well under intense terahertz field are
investigated by using a density matrix approach. The results show that the
terahertz fields with different frequencies cause the distinct
modulations of the intersubband absorptions. The
terahertz-induced sideband and Autler--Towns splitting in the
absorption spectrum are obtained, respectively for the
terahertz-photon energy below and close to the transition energy
between the ground and first excited state.

We develop a Monte Carlo (MC) tool incorporated with the three-subband
approximation model to investigate the in-plane spin-polarized transport in
GaAs/GaAlAs quantum well. Using the tool, the effects of the electron
occupation of higher subbands and the intersubband scattering on the spin
dephasing have been studied. Compared with the corresponding results of the
simple one-subband approximation model, the spin
dephasing length is reduced four times under 0.125\,kV/cm of driving electric field at
300K by the MC tool incorporated with the three-subband approximation model,
indicating that the three-subband approximation model predicts significantly
shorter spin dephasing length with temperature increasing. Our simulation
results suggest that the effects of the electron occupation of higher
subbands and the intersubband scattering on the spin-dependent transport of
GaAs 2-dimensional electron gas need to be considered when the driving
electric field exceeds the moderate value and the lattice temperature is
above 100K. The simulation by using the MC tool incorporated with the
three-subband approximation
model also indicates that, under a certain driving electric field and
lattice temperature, larger channel widths cause spins to be depolarized faster.
Ranges of the three components of the spins are different for three
different injected spin polarizations due to the anisotropy of spin--orbit
interaction.