The convergent iterative procedure for solving the groundstate Schr?dinger
equation is extended to derive the excitation energy and the wavefunction of the
low-lying excited states. The method is applied to the one-dimensional quartic
potential problem. The results show that the iterative solution converges rapidly
when the coupling g is not too small.

In this paper, we derive an explicit analytic expression of the
relative entropy between two general Gaussian states. In the
restriction of the set for Gaussian states and with the help of
relative entropy formula and Peres--Simon separability criterion,
one can conveniently obtain the relative entropy entanglement for
Gaussian states. As an example, the relative entanglement for a
two-mode squeezed thermal state has been obtained.

The trace identity is extended to the quadratic-form identity. The Hamiltonian
structures of the multi-component Guo hierarchy, integrable coupling of Guo
hierarchy and (2+1)-dimensional Guo hierarchy are obtained by the quadratic-form
identity. The method can be used to produce the Hamiltonian structures of the other
integrable couplings or multi-component hierarchies.

The EI Ni?/La Ni?a-Southern Oscillation (ENSO) is an interannual phenomenon
involved in the tropical Pacific Ocean--atmosphere interactions. In this paper, an
asymptotic method of solving the nonlinear equation for the ENSO model is created.
And based on a class of oscillator of the ENSO model, the approximate solution of a
corresponding problem is studied by employing the method of homotopic mapping. It is
proved from the results that the homotopic method can be used for analysing the sea
surface temperature anomaly in the equatorial eastern Pacific and the thermocline
depth anomaly of the atmosphere--ocean oscillation for the ENSO model.

In this paper, the stability with respect to partial variables for the
Birkhoff system is studied. By transplanting the results of the partial
stability for general systems to the Birkhoff system and constructing a
suitable Liapunov function, the partial stability of the system can be
achieved. Finally, two examples are given to illustrate the application of
the results.

The perturbations to symmetries and adiabatic invariants for nonconservative systems
of generalized classical mechanics are studied. The exact invariant in the form of
Hojman from a particular Lie symmetry for an undisturbed system of generalized
mechanics is given. Based on the concept of high-order adiabatic invariant in
generalized mechanics, the perturbation to Lie symmetry for the system under the
action of small disturbance is investigated, and a new adiabatic invariant for the
nonconservative system of generalized classical mechanics is obtained, which can be
called the Hojman adiabatic invariant. An example is also given to illustrate the
application of the results.

In this paper, we present a linear optical scheme for optimal
unambiguous discrimination among nonorthogonal quantum states in
terms of the multiple-rail and polarization representation of a
single photon. In our scheme, discriminated quantum states are
expressed by using the spatial degree of freedom of a single photon
while the polarization degree of freedom of the single photon is
used to act as an auxiliary qubit. The optical components used in
our scheme are only passive linear optical elements such as
polarizing beam splitters, wave plates, polarizers, single photon
detectors, and single photon source.

The dissipative dynamic stability is investigated of dark solitons
in elongated Bose--Einstein condensates that can be described by the
Gross--Pitaevskii equation including an additional term. Based on
the direct perturbation theory for the nonlinear Schr?dinger
equation, the dependence of the soliton velocity on time is
explicitly given, and the shape of dark solitons remaining unchanged
under the dissipative condition is confirmed theoretically for the
first time. It is found that the dynamically stable dark solitons
turn out to be thermodynamically unstable.

Based on the state equation of an ideal quantum gas, the regenerative loss of a
Stirling engine cycle working with an ideal quantum gas is calculated. Thermal
efficiency of the cycle is derived. Furthermore, under the condition of quantum
degeneracy, several special thermal efficiencies are discussed. Ratios of thermal
efficiencies versus the temperature ratio and volume ratio of the cycle are made. It
is found that the thermal efficiency of the cycle not only depends on high and low
temperatures but also on maximum and minimum volumes. In a classical gas state
the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal
quantum gas state the thermal efficiency of the cycle is smaller than that of the
Carnot cycle. This will be significant for deeper understanding of the gas Stirling
engine cycle.

The ground-state properties of a system with a small number of interacting bosons
over a wide range of densities are investigated. The system is confined in a
two-dimensional isotropic harmonic trap, where the interaction between bosons is
treated as a hard-core potential. By using variational Monte Carlo method, we
diagonalize the one-body density matrix of the system to obtain the ground-state
energy, condensate wavefunction and the condensate fraction. We find that in the
dilute limit the depletion of central condensate in the 2D system is larger than in
a 3D system for the same interaction strength; however as the density increases, the
depletion at the centre of 2D trap will be equal to or even lower than that at the
centre of 3D trap, which is in agreement with the anticipated in Thomas--Fermi
approximation. In addition, in the 2D system the total condensate depletion is still
larger than in a 3D system for the same scattering length.

In this paper, a new method for controlling projective synchronization in coupled
chaotic systems is presented. The control method is based on a partially linear
decomposition and negative feedback of state errors. Firstly, the synchronizability
of the proposed projective synchronization control method is proved mathematically.
Then, three different representative examples are discussed to verify the
correctness and effectiveness of the proposed control method.

Synchronization of a hyperchaotic Lorenz system is discussed using
passive control. Based on the properties of a passive system, a
passive controller is designed and the synchronization between two
hyperchaotic Lorenz systems under different initial conditions is
realized. Simulation results show the proposed synchronization
method to be effective.

Using the Faddeev--Jackiw (FJ) quantization method,this paper treats the CP^{1} nonlinear sigma model with Chern--Simons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac's method.

The multi-reference configuration interaction method and aug-cc-pvqz (AVQZ) have
been used to calculate potential energy curves (PECs) of the singlet and triplet
states of the $\prod _{\rm u}$ and $\prod _{\rm g}$ symmetry of B$_{2}^{ + + }$. All
of the four states (^{1}!\prod _{\rm u}$, $^{ 1\!}\prod _{\rm g}$, $^{ 3\!}\prod
_{\rm u }$ and $^{3\!}\prod _{\rm g})$ are found to be metastable states, though the
potential well of $^{3\!}\prod _{\rm u }$ symmetry is very shallow. Based on the
PECs, the analytical potential energy functions (APEFs) of these states have been
fitted using the least square fitting method and two models of function. The
spectroscopic parameters of each state are also calculated, and are compared with
other investigations in the literature. The credibility and veracity of the two
functions are evaluated. Some ideas to improve the fitting accuracy are presented.
Also the vibrational levels for each state are predicted by solving the
Schr\"{o}dinger equation of nuclear motion.

A detailed study of the mechanisms of the emissions of pions and protons
in the forward
and backward hemispheres in 4.5 A GeV/c oxygen-emulsion interactions has
been carried out.
The correlations between the multiplicities of secondary charged
particles in the backward
and forward hemispheres are investigated.

The method of time-dependent quantum wave packet dynamics is used to calculate the
femtosecond pump--probe photoelectron spectra and study the wave packet dynamic
processes of the double-minimum potential state 6^{1}∑^{+} of NaK in intense
laser fields. The evolutions of the wave packet and the photoelectron energy spectra
with time and internuclear distance are described in detail. The wave packet dynamic
information of the 6^{1}∑^{+} state can be extracted from the photoelectron
energy spectra.

The resolution and classical noise in ghost
imaging with a classical thermal light are investigated
theoretically. For ghost imaging with a Gaussian Schell model
source, the dependences of the resolution and noise on the spatial
coherence of the source and the aperture in the imaging system are
discussed and demonstrated by using numerical simulations.
The results show that an incoherent source and a large aperture
will lead to a good image quality and small noise.

The quality of the novelty filter image is investigated at different
intensities of the incident blue and yellow beams irradiating a
bacteriorhodopsin (bR) film. The relationship between the transmitted blue
beams and the incident yellow beams is established. The results show that
the contrast of the novelty filter image depends on the lifetime of longest
lived photochemical state (M state). These results enable one to identify
the direction of a moving object and to improve the quality of the novel
filter image by prolonging the lifetime of M state.

We investigate the entanglement in a system of two coupling atoms
interacting with a single-mode field
by means of quantum information entropy theory.
The quantum entanglement between the two atoms and the coherent field is discussed by using
the quantum reduced entropy,
and the entanglement between the two coupling atoms is also investigated
by using the quantum relative entropy.
In addition, the influences of the atomic dipole--dipole interaction
intensity and
the average photon number of the coherent field on the degree of the entanglement is examined.
The results show that the evolution of the degree of entanglement between the two atoms
and the field is just opposite to that of the degree of entanglement between the two atoms.
And the properties of the quantum entanglement in the system rely on the
atomic dipole--dipole
interaction and the average photon number of the coherent field.

A compact, efficient and high-power laser diode (LD) single-end-pumped Nd:YVO_{4}
laser with continuous-wave emission at 1342 nm is reported. With a single crystal
single-end-pumped by fibre-coupled LD array, an output power of 7.36W is obtained
from the laser cavity of concave-convex shape, corresponding to an
optical-to-optical efficiency of 32.8%. The laser is operated in TEM_{00} mode
with small rms amplitude noise of 0.3%. The influences of the Nd concentration,
transmissivity of the output mirror and the cavity length on the output power have
been
studied experimentally.

A stable continuous wave mode-locked picosecond Ti:sapphire laser by using a fast
semiconductor saturable absorber mirror (SESAM) is demonstrated. The laser delivers
pulse width of 20 ps at a central wavelength of 813 nm and a repetition rate of 100
MHz. The maximum output power is 1.34 W with pump power of 7 W which corresponds to
an optical--optical conversion efficiency of 19.1%.

The main characteristics of the third harmonic emission generated by
femtosecond laser pulses propagating in air are investigated by numerically
solving the coupled nonlinear Schr?dinger equations. Strong third
harmonic emission is observed with a maximum conversion efficiency as high
as 0.43%. The on-axis phase difference between fundamental beam and third
harmonic is investigated. The result is in good agreement with the
phase-locking mechanism. Dependence of the conversion of third harmonic
emission on focusing conditions is also studied. The results are also
compared with those of experiments.

Based on Schaaff's collision factor theory (CFT) in liquids, the equations for
nonlinear ultrasonic parameters in both organic liquid and binary organic liquid
mixtures are deduced. The nonlinear ultrasonic parameters, including pressure
coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic
parameter B/A in both organic liquid and binary organic liquid mixtures, are
evaluated for comparison with the measured results and data from other sources. The
equations show that the coefficient of ultrasonic velocity and nonlinear acoustic
parameter B/A are closely related to molecular interactions. These nonlinear
ultrasonic parameters reflect some information of internal structure and outside
status of the medium or mixtures. From the exponent of repulsive forces of the
molecules, several thermodynamic parameters, pressure and temperature of the medium,
the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be
evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary
organic liquid mixtures, there is no need to know the nonlinear acoustic parameter
B/A of the components. Obviously, the equation reveals the connection between the
nonlinear ultrasonic nature and internal structure and outside status of the
mixtures more directly and distinctly than traditional mixture law for B/A, e.g.
Apfel's and Sehgal's laws for liquid binary mixtures.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

This paper investigates the intensity tuning characteristics of a double
longitudinal modes He--Ne laser subjected to optical feedback. The intensity
undulations of the total light and the two modes are observed for different external
cavity length. Two modulations of the internal cavity length are performed. One is
only for the internal cavity length being modulated and the other is for both the
internal and the external cavity length being modulated. The undulation frequency of
the total light is found to be determined by the ratio of external cavity length to
internal cavity length in both modulations. When the external cavity length is
integral times of the internal cavity length, the fringe frequency of the total
light could be seven or even more times of that in conventional optical feedback. A
simple theoretical analysis is presented, which is in good agreement with the
experimental results. The potential use of the experimental results is also
discussed.

A helix type slow wave structure filled with plasma is immersed in a strong
longitudinal magnetic field. Taking into account the effect of the plasma and the
dielectric, the system is separated radially into three regions. By means of
the sheath model and Maxwell equation, the distribution of the electromagnetic
field is established. Using the boundary conditions of each region, the dispersion
relation of the slow wave structure is derived. The trend of change for the radial
profile of the axial electric field is analysed respectively in different plasma
densities, plasma column radius and dielectric constant by numerical computation.
Some useful results are obtained on the basis of the discussion.

This paper shows that the standing, backward- and forward-accelerated large
amplitude relativistic electromagnetic solitons induced by intense laser pulse in
long underdense collisionless homogeneous plasmas can be observed by particle
simulations. In addition to the inhomogeneity of the plasma density, the
acceleration of the solitons also depends upon not only the laser amplitude but also
the plasma length. The electromagnetic frequency of the solitons is between about
half and one of the unperturbed electron plasma frequency. The electrostatic field
inside the soliton has a one-cycle structure in space, while the transverse electric
and magnetic fields have half-cycle and one-cycle structure respectively. Analytical
estimates for the existence of the solitons and their electromagnetic frequencies
qualitatively coincide with our simulation results.

A preliminary experiment triggering a plasma current quench by laser ablation of
high-Z impurities has been performed in the HL-1M tokamak. The injection of
impurities with higher electric charges into tokamak plasmas can increase the
radiation cooling of the plasma. Resistive, highly radiating plasma formed prior to
the thermal quench can dissipate both the thermal and magnetic energies, which is
possibly a simple and potential approach to reducing significantly the plasma
thermal energy and magnetic energy before a disruption thereby a safe plasma
termination is obtained.

Zhang Fa-Qiang, Li Zheng-Hong, Xu Ze-Ping, Xu Rong-Kun, Yang Jian-Lun, Guo Cun, Xia Guang-Xin, Chen Jin-Chuan, Song Feng-Jun, Ning Jia-Min, Wang Zhen, Xue Fei-Biao, Li Lin-Bo, Qin Yi, Ying Chun-Tong,

Chin. Phys. B 2006, 15 (9): 02058; doi: 10.1088/1009-1963/15/9/028
Full Text: PDF (728KB) (
735
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Z-pinch experiments with two arrays consisting, respectively, of 32
4-μm- and 6-μm-diameter tungsten wires have been carried out on
QiangGuang-1 facility with a current rising up to 1.5MA in 80ns. At early
time of implosion, x-ray framing images show that the initial emission comes
from the central part of arrays, and double clear emission rings, drifting
to the anode and the cathode at 5×10^{6}cm/s and 2.4×10^{7}cm/s respectively, are often produced near the electrodes. Later,
in a 4-μm-diameter tungsten wire array, filamentation caused by ohmic
heating is prominent, and more than ten filaments have been observed. A
radial inward shift of arrays starts at about 30\,ns earlier than the
occurrence of the x-ray peak power for both kinds of arrays, and the
shrinkage rate of emission region is as high as 1.7×10^{7}cm/s in
a 4-μm-diameter tungsten wire array, which is two times higher than
that in a 6-μm one. Emission from precursor plasmas is observed in
implosion of 6-μm-diameter tungsten wire arrays, but not in implosion
of a 4-μm-diameter tungsten wire array. Whereas, in a 4-μm-diameter tungsten wire array, the soft x-ray emission shows the growth of
m=1 instability in the plasma column, which is caused by current. The
reasons for the discrepancy between implosions of 4-μm- and 6-μm-diameter tungsten wire arrays are explained.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

In addition to the phonon variable there is the phason variable in
hydrodynamics for quasicrystals. These two kinds of hydrodynamic
variables have different transformation properties. The phonon
variable transforms under the vector representation, whereas the
phason variable transforms under another related representation.
Thus, a basis (or a set of basis functions) in the representation
space should include such two kinds of variables. This makes it more
difficult to determine the physical property tensors of
quasicrystals. In this paper the group-theoretical method is given
to determine the physical property tensors of quasicrystals. As an
illustration of this method we calculate the third-order elasticity
tensors of quasicrystals with five-fold symmetry by means of basis
functions. It follows that the linear phonon elasticity is
isotropic, but the nonlinear phonon elasticity is anisotropic for
pentagonal quasicrystals. Meanwhile, the basis functions are
constructed for all noncrystallographic point groups of
quasicrystals.

Xiang Yan-Juan, Wu Xiao-Chun, Liu Dong-Fang, Zhang Zeng-Xing, Song Li, Zhao Xiao-Wei, Liu Li-Feng, Luo Shu-Dong, Ma Wen-Jun, Shen Jun, Zhou Wei-Ya, Zhou Jian-Jun, Wang Chao-Ying, Wang Gang

Chin. Phys. B 2006, 15 (9): 02080; doi: 10.1088/1009-1963/15/9/030
Full Text: PDF (1211KB) (
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Arrays of noble metal nanoparticles show potential applications in (bio-)sensing,
optical storage, surface-enhanced spectroscopy, and waveguides. For all such
potential devices, controlling the size, morphology, and interparticle spacing of
the nanoparticles is very important. Here, we combine seed-mediated growth with
nanosphere lithography to study the controllable growth of gold nanoparticles (Au
NPs), in which the self-assembly monolayer of polystyrene (PS) on a silicon surface
is used to guide the modification of alkanesilanes and the subsequent adsorption of
gold seeds; seed-mediated growth is applied to controlling the morphology and size
of Au NPs. The size of adsorption region (determining the number of adsorbed gold
seeds) is controlled by etching PS microspheres with oxygen plasma or annealing PS
microspheres at the glass transition temperature. The size and morphology of the Au
NPs are controlled by changing growth conditions. In such a way, we have achieved
the dual control of the obtained Au NPs. Preliminary results show that this strategy
holds a great promise. This approach can also be extended to a wide range of
materials and substrates.

The mosaic structure in a Ni-based single-crystal superalloy is simulated by
molecular dynamics using a potential employed in a modified analytic embedded atom
method. From the calculated results we find that a closed three-dimensional misfit
dislocation network, with index of $\langle 011\rangle${\{}100{\}} and the side
length of the mesh 89.6\,{\AA}, is formed around a cuboidal $\gamma '$ precipitate.
Comparing the simulation results of the different mosaic models, we find that the
side length of the mesh only depends on the lattice parameters of the $\gamma $ and
$\gamma '$ phases as well as the $\gamma $/$\gamma '$ interface direction, but is
independent of the size and number of the cuboidal $\gamma '$ precipitate. The
density of dislocations is inversely proportional to the size of the cuboidal
$\gamma '$ precipitate, i.e.~the amount of the dislocation is proportional to the
total area of the $\gamma $/$\gamma '$ interface, which may be used to explain the
relation between the amount of the fine $\gamma '$ particles and the creep rupture
life of the superalloy. In addition, the closed three-dimensional networks assembled
with the misfit dislocations can play a significant role in improving the mechanical
properties of superalloys.

The phonon spectrum and the related thermodynamic properties of
microcracks in bcc-Fe are studied with the recursion method by using
the Finnis--Sinclair
(F--S) N-body potential. The initial configuration of the microcracks is established
from an anisotropic linear elastic solution and relaxed to an
equilibrium by molecular dynamics method. It is shown that the local
vibrational density of states of the atoms near a crack tip is
considerably different from the bulk phonon spectrum, which is
closely associated with the local stress field around the crack tip;
meanwhile, the local vibrational energies of atoms near the crack
tip are higher than those of atoms in a perfect crystal. These
results imply that the crack tip zone is in a complex stress state
and closely related to the structure evolution of cracks. It is also
found that the phonon excitation is a kind of local effect induced
by microcracks. In addition, the microcrack system has a higher
vibrational entropy, which reflects the character of phonon spectrum
related to the stress field induced by cracks.

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

The effect of an electric field E on a narrow quantum ring that contains two
electrons and is threaded by a magnetic flux B has been investigated. Localization
of the electronic distribution and suppression of the Aharonov--Bohm oscillation
(ABO) are found in the two-electron ring, which are similar to those found in a
one-electron ring. However, the period of ABO in a two-electron ring is reduced by
half compared with that in a one-electron ring. Furthermore, during the variation of
B, the persistent current of the ground state may undergo a sudden change in sign.
This change is associated with a singlet--triplet transition and has no counterpart
in one-electron rings. For a given E, there exists a threshold of energy. When
the energy of the excited state exceeds the threshold, the localization would
disappear and the ABO would recover. The value of the threshold is proportional to
the magnitude of E. Once the threshold is exceeded, the persistent current is much
stronger than the current of the ground state at E=0.

In the harmonic approximation, the atomic force constants are derived and the phonon
dispersion curves along four major symmetry directions [00$\zeta $], [0$\zeta \zeta
$], [$\zeta \zeta \zeta $] and [0$\zeta $1] (or $\De $, $\Si $, $\La $ and $Z$ in
group-theory notation) are calculated for four noble metals Cu, Ag, Au and Pt by
combining the modified analytic embedded atom method (MAEAM) with the theory of
lattice dynamics. A good agreement between calculations and measurements, especially
for lower frequencies, shows that the MAEAM provides a reasonable description of
lattice dynamics in noble metals.

This paper presents a theory on accurately analysing the dispersion relation and the
interaction impedance of electromagnetic waves propagating through a helical groove
waveguide with arbitrary groove shape, in which the complex groove profile is
synthesized by a series of rectangular steps. By introducing the influence of
high-order evanescent modes on the connection of any two neighbouring steps by an
equivalent susceptance under a modified admittance matching condition, the
assumption of the neglecting discontinuity capacitance in previously published
analysis is avoided, and the accurate dispersion equation is obtained by means of a
combination of field-matching method and admittance-matching technique. The validity
of this theory is proved by comparison between the measurements and the numerical
calculations for two kinds of helical groove waveguides with different groove
shapes.

We have studied the quantum transport of electrons in a three-step
single-barrier AlGaAs heterostructure under electric field. Using the
quantum transmitting boundary method and Tsu--Esaki approach, we have
calculated the transmission coefficient and current--voltage
characteristic.
The difference of the effective mass among the three barriers
is taken into account. Effects of the barrier width on transmission
coefficient and peak-to-valley current ratios are examined. The largest
peak-to-valley current ratio is obtained when the ratio of widths of the left,
middle, and right barrier is fixed at 4:2:1. The calculated results may
be helpful for designing devices based on three-step barrier
heterostructures.

Due to the zero dispersion point at 1.3μm in optical fibres, 1.3-μm
InGaAsP/InP laser diodes have become main light sources in fibre communication
systems recently. Influences of quantum noises on direct-modulated properties of
single-mode 1.3-μm InGaAsP/InP laser diodes are investigated in this article.
Considering the carrier and photon noises and the cross-correlation between the two
noises, the power spectrum of the photon density and the signal-to-noise ratio (SNR)
of the direct-modulated single-mode laser system are calculated using the linear
approximation method. We find that the stochastic resonance (SR) always appears in
the dependence of the SNR on the bias current density, and is strongly affected by
the cross-correlation coefficient between the carrier and photon noises, the
frequency of modulation signal, and the photon lifetime in the laser cavity. Hence,
it is promising to use the SR mechanism to enhance the SNR of direct-modulated
InGaAsP/InP laser diodes and improve the quality of optical fibre communication
systems.

Quantum-state engineering, i.e. active manipulation over the coherent dynamics of
suitable quantum-mechanical systems, has become a fascinating prospect of modern
physics. Here we discuss the dynamics of two interacting electrons in a coupled
quantum dot driven by an external electric field. The results show that the two
quantum dots can be used to prepare a maximally entangled Bell state by changing
the strength and duration of an oscillatory electric field. Different from the
suggestion made by Loss \textit et al (1998 Phys. Rev. A 57 120, the
present entanglement involves the spatial degree of freedom for the two electrons.
We also find that the coherent tunnelling suppression discussed by Grossmann
\textit et al (1991 Phys. Rev. Lett. 67 516 persists in the
two-particle case: i.e. two electrons initially localized in one dot can remain
dynamically localized, although the strong Coulomb repulsion prevents them from
behaving so. Surprisingly, the interaction enhances the degree of localization to a
large extent compared with that in the non-interacting case. This phenomenon is
referred to as the Coulomb-enhanced dynamical localization.

The Ti--Al ohmic contact to n-type 6H-SiC has been fabricated. An array of TLM
(transfer length method) test patterns with Au/Ti/Al/Ti/SiC structure is formed on
N-wells created by P^{+} ion implantation into Si-faced p-type 6H-SiC epilayer.
The specific contact resistance \rho _{c} as low as 8.64×10^{-6}\Omega\cdot cm^{2} is achieved after annealing in N_{2} at
900℃ for 5\,min. The sheet resistance R_{sh} of the implanted layers
is 975\Omega/\sqcap\!\!\!\!\sqcup. X-ray diffraction (XRD) analysis shows the
formation of Ti_{-3}SiC_{2} at the metal/n-SiC interface after thermal annealing,
which is responsible for the low resistance contact.

In this paper the values of the crystalline-electric-field
parameters A_{nm} for R_{2}Fe_{17} and
R_{2}Fe_{17}H_{3} (R=Tb,Ho,Er) are evaluated by fitting
calculations to the magnetization curves measured on the single
crystal at several temperatures. The fitted A_{nm} for
R_{2}Fe_{17} are strikingly different from those for the
corresponding R_{2}Fe_{17}H_{3}. The energy gaps between the
lowest four energy levels for Ho ions in Ho_{2}Fe_{172} can be
reproduced by using the fitted A_{nm} and exchange field
2μ_{B}H_{ex}, which estimated from the fit of the
temperature dependence of the spontaneous magnetization combined
with inelastic neutron scattering experiment.

We have performed a full numerical calculation of the Franz--Keldysh (FK)
effect on magnetoexcitons in a bulk GaAs semiconductor. By employing an
initial value method in combination with the application of a perfect matched
layer, the numerical effort and storage size are dramatically reduced due to
a significant reduction in both computed domain and number of base
functions. In the absence of an electric field, the higher magnetoexcitonic
peaks show distinct Fano lineshape due to the degeneracy with continuum states
of the lower Landau levels. The magnetoexcitons that belong to the zeroth
Landau level remain in bound states and lead to Lorentzian lineshape, because they
are not degenerated with continuum states. In the presence of an electric
field, the FK effect on each magnetoexcitonic resonance can be identified for
high magnetic fields. However, for low magnetic fields, the FK oscillations
dominate the spectrum structure in the vicinity of the bandgap edge and the
magnetoexcitonic resonances dominate the spectrum structure of higher
energies.
In the moderate electric fields, the interplay of FK effect and
magnetoexcitonic resonance leads to a complex and rich structure in the
absorption spectrum.

Er^{3+}-doped tellurite glasses with molar compositions of
xNb_{2}O_{5}-(14.7-x)Na_{2}O--10ZnO--5K_{2}O--10GeO_{2}--
60TeO_{2}--0.3Er_{2}O_{3}
(x=0, 3, 5, 7 and 9) have been investigated for developing 1.5~μm
fibre and planar amplifiers. The effects of Nb_{2}O_{5} on the thermal stability
and optical properties of Er^{3+}-doped tellurite glasses have been discussed.
It is noted that the incorporation of Nb_{2}O_{5} (x=5) increases the thermal
stability of tellurite glasses significantly. Er^{3+}-doped niobium tellurite
glasses exhibit a large stimulated emission cross-section (7.2\times 10^{-21}-
10.7×10^{-21}~cm^{2} and the gain bandwidth, FWHM×\sigma_{e}^{\rm peak} (274\times 10^{-28} - 480×10^{-28}~cm^{3}), which are
significantly higher than that of silicate and phosphate glasses. In addition, the
intensity of upconversion luminescence of the Er^{3+}-doped niobium tellurite
glasses decreases rapidly with increasing Nb_{2}O_{5} content. As a result,
Er^{3+}-doped niobium tellurite glasses might be a potential candidate for
developing laser or optical amplifier devices.

Using transmission electron microscopy (TEM) and x-ray diffraction
analysis, we have studied the structural and morphological evolution
of highly Er/Yb co-doped Al_{2}O_{3} films in the temperature
range from $600\,^{\circ}\mkern-1mu$C--900$\,^{\circ}\mkern-1mu$C.
By comparison with TEM observation, the annealing behaviours of
photoluminescence (PL) emission and optical loss were found to have
relation to the structure and morphology. The increase of PL
intensity and optical loss above 800$\,^{\circ}\mkern-1mu$C might
result from the crystallization of amorphous Al_{2}O_{3} films.
Based on the study on the structure and morphology, a rate equation
propagation model of a multilevel system was used to calculate the
optical gains of Er-doped Al_{2}O_{3} planar waveguide
amplifiers involving the variation of PL efficiency and optical loss
with annealing temperature. It was found that the amplifiers had an
optimized optical gain at the temperature corresponding to the
minimum of optical loss, rather than at the temperature
corresponding to the maximum of PL efficiency, suggesting
that the optical loss is a key factor for determining the optical gain of an
Er-doped Al_{2}O_{3} planar waveguide amplifier.

8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Based on the effective medium approximation theory of composites, the
whitecap-covered sea surface is treated as a medium layer of dense seawater
droplets and air. Two electromagnetic scattering models of randomly rough
surface are applied to the investigation of microwave backscattering of breaking
waves driven by strong wind. The shapes of seawater droplets are considered
by calculating the effective dielectric constant of the whitecap layer. The
responses of seawater droplets shapes, such as sphere and ellipsoid, to the
backscattering coefficient are discussed. Numerical results of the models are in
good agreement with the experimental measurements of horizontally and
vertically polarized backscattering at microwave frequency 13.9GHz and
different incidence angles.

Due to global warming, the general circulation, underlying surfaces characteristics,
and geophysical and meteorological elements all show evident secular trends. This
paper points out that when calculating the correlation of two variables containing
their own obvious secular trends, the interannual correlation characteristics
between the two variables may be distorted (overestimated or underestimated).
Numerical experiments in this paper show that if two variables have opposite secular
trends, the correlation coefficient between the two variables is reduced (the
positive correlation is underestimated, or the negative correlation is
overestimated); and if the two variables have the same sign of secular trends, the
correlation coefficient between the two variables is increased (the positive
correlation is overestimated, or the negative correlation is underestimated).
Numerical experiments also suggest that the effect of secular trends on the
interannual correlation of the two variables is interchangeable, that is to say, as
long as the values of the two trends are not changed, the two variables interchange
their positions, and the effect of the secular trends on the interannual correlation
coefficient of the two variables remains the same. If the two variables have the
same-(opposite-) sign trends, the effect of secular trends on the interannual
correlation coefficient is more (less) distinctive. A meteorological example is
given.

Evidence for the long-term optical curve variability and colour behaviour of the BL
Lac object Mkn 421 is presented. Our results show that the amplitude of the optical
variations of Mkn 421 is only about {\Delta} B=4.7 magnitude in the B-band for
its photometric history from 1899 to 2002. The results of optical photometric
monitoring of the Mkn 421 from April 2000 to Jan 2002 are provided. During our
observation, Mkn 421 shows significant rapid variations and exhibits short time
variability of 2.42 hours in the B band. A strong correlation between the B-V
colour index and the magnitude in the B band is found. Our charge coupled device
(CCD) photometry of Mkn 421 shows that the measured results are in good agreement
with the predicted optical variability period of about 23 years.

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