Chin. Phys. B
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CN 11-5639/O4
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Chin. Phys. B  
  Chin. Phys. B--2007, Vol.16, No.9
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GENERAL

An integrable Hamiltonian hierarchy and associated integrable couplings system

Chen Xiao-Hong, Xia Tie-Cheng, Zhu Lian-Cheng
Chin. Phys., 2007, 16 (9): 2493-2497 doi: 10.1088/1009-1963/16/9/001
Full Text: [PDF 105 KB] (Downloads:558)
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This paper establishes a new isospectral problem. By making use of the Tu scheme, a new integrable system is obtained. It gives integrable couplings of the system obtained. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented.

Controlling disease spread on networks with feedback mechanism

Wang Li, Yan Jia-Ren, Zhang Jian-Guo, Liu Zi-Ran
Chin. Phys., 2007, 16 (9): 2498-2502 doi: 10.1088/1009-1963/16/9/002
Full Text: [PDF 409 KB] (Downloads:451)
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Many real-world networks have the ability to adapt themselves in response to the state of their nodes. This paper studies controlling disease spread on network with feedback mechanism, where the susceptible nodes are able to avoid contact with the infected ones by cutting their connections with probability when the density of infected nodes reaches a certain value in the network. Such feedback mechanism considers the networks' own adaptivity and the cost of immunization. The dynamical equations about immunization with feedback mechanism are solved and theoretical predictions are in agreement with the results of large scale simulations. It shows that when the lethality $\alpha$ increases, the prevalence decreases more greatly with the same immunization $g$. That is, with the same cost, a better controlling result can be obtained. This approach offers an effective and practical policy to control disease spread, and also may be relevant to other similar networks.

Asymptotical solutions of coupled nonlinear Schr?dinger equations with perturbations

Cheng Xue-Ping, Lin Ji, Ye Li-Jun
Chin. Phys., 2007, 16 (9): 2503-2509 doi: 10.1088/1009-1963/16/9/003
Full Text: [PDF 1018 KB] (Downloads:446)
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In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schr\"{odinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear Schr\"{odinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.

Exponential--fraction trial function method to the 5th-order mKdV equation

Li Ya-Zhou, Feng Wei-Gui, Li Kai-Ming, Lin Chang
Chin. Phys., 2007, 16 (9): 2510-2513 doi: 10.1088/1009-1963/16/9/004
Full Text: [PDF 269 KB] (Downloads:432)
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This paper obtains some solutions of the 5th-order mKdV equation by using the exponential--fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.

Some new exact solutions to the Burgers--Fisher equation and generalized Burgers--Fisher equation

Jiang Lu, Guo Yu-Cui, Xu Shu-Jiang
Chin. Phys., 2007, 16 (9): 2514-2522 doi: 10.1088/1009-1963/16/9/005
Full Text: [PDF 469 KB] (Downloads:858)
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Some new exact solutions of the Burgers--Fisher equation and generalized Burgers--Fisher equation have been obtained by using the first integral method. These solutions include exponential function solutions, singular solitary wave solutions and some more complex solutions whose figures are given in the article. The result shows that the first integral method is one of the most effective approaches to obtain the solutions of the nonlinear partial differential equations.

Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

Xie Li, Lei Yin-Zhao
Chin. Phys., 2007, 16 (9): 2523-2536 doi: 10.1088/1009-1963/16/9/006
Full Text: [PDF 270 KB] (Downloads:338)
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The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

Exciton--polaritons in ternary mixed crystals

Liu Li, Liang Xi-Xia, Bao Jin
Chin. Phys., 2007, 16 (9): 2537-2543 doi: 10.1088/1009-1963/16/9/007
Full Text: [PDF 195 KB] (Downloads:411)
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In this paper the bulk exciton polaritons in ternary mixed crystals (TMCs) are investigated in the Born--Huang approximation. The numerical results of the polariton frequencies as functions of the wave-vector and the compositions for ternary mixed crystals Al$_{x$Ga$_{1 - x$As, Cd$_{x$Zn$_{1 - x$Se, and Al$_{x$Ga$_{1 - x$N are obtained and discussed. The new dispersion characteristics for exciton--polaritons in TMC systems are found in comparison with binary crystals. The splitting of the two branches of exciton--polariton frequencies varies nonlinearly with the composition of TMCs and has a minimum in the long-wavelength range.

Density matrix of two interacting particles with kinetic coupling derived in bipartite entangled state representation

Guo Qin
Chin. Phys., 2007, 16 (9): 2544-2548 doi: 10.1088/1009-1963/16/9/008
Full Text: [PDF 113 KB] (Downloads:373)
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A density matrix is usually obtained by solving the Bloch equation, however only a few Hamiltonians' density matrices can be analytically derived. The density matrix for two interacting particles with kinetic coupling is hard to derive by the usual method due to this coupling; this paper solves this problem by using the bipartite entangled state representation.

Secure deterministic communication scheme based on quantum remote state preparation

Guo Ying, Chen Zhi-Gang, Zeng Gui-Hua
Chin. Phys., 2007, 16 (9): 2549-2556 doi: 10.1088/1009-1963/16/9/009
Full Text: [PDF 325 KB] (Downloads:534)
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Based on the techniques of the quantum remote state preparation via a deterministic way, this paper proposes a quantum communication scheme to distribute the secret messages in two phases, i.e., the carrier state checking phase and the message state transmitting phase. In the first phase, the secret messages are encoded by the sender using a stabilizer quantum code and then transmitted to the receiver by implementing three CNOT gates. In the second phase, the communicators check the perfectness of the entanglement of the transmitted states. The messages can be distributed to the receiver even if some of the transmitted qubits are destroyed.

Controlled teleportation of high-dimension quantum-states with generalized Bell-state measurement

Zhan You-Bang
Chin. Phys., 2007, 16 (9): 2557-2562 doi: 10.1088/1009-1963/16/9/010
Full Text: [PDF 107 KB] (Downloads:788)
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In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.

Probabilistic teleportation of an arbitrary pure state of two atoms

Yang Zhen-Biao, Wu Huai-Zhi, Su Wan-Jun
Chin. Phys., 2007, 16 (9): 2563-2568 doi: 10.1088/1009-1963/16/9/011
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In the context of microwave cavity QED, this paper proposes a new scheme for teleportation of an arbitrary pure state of two atoms. The scheme is very different from the previous ones which achieve the integrated state measurement, it deals in a probabilistic but simplified way. In the scheme, no additional atoms are involved and thus only two atoms are required to be detected. The scheme can also be used for the teleportation of arbitrary pure states of many atoms or two-mode cavities.

The transfer of the quantum correlation from two-mode nonclassical state field to the supercurrents in two distant SQUID rings

Peng Zhao-Hui, Zou Jian, Shao Bin
Chin. Phys., 2007, 16 (9): 2569-2577 doi: 10.1088/1009-1963/16/9/012
Full Text: [PDF 1122 KB] (Downloads:542)
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We have considered two distant mesoscopic superconducting quantum interference device (SQUID) rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function $C_{\rm AB}$. We show that when the parameter $\alpha$ is very small for the separable state with the density matrix $\hat {\rho } = (\left| {\alpha , - \alpha } \right\rangle \left\langle {\alpha , - \alpha } \right| + \left| { - \alpha ,\alpha } \right\rangle \left\langle { - \alpha ,\alpha } \right|) / 2$ and entangled coherent state (ECS) $\left| u \right\rangle = N_1 (\left| {\alpha , - \alpha } \right\rangle + \left| { - \alpha ,\alpha } \right\rangle )$ fields, the dynamic behaviours of the normalized correlation function $C_{\rm AB}$ are similar, but it is quite different for the entangled coherent state $\left| {u}' \right\rangle = N_2 (\left| {\alpha , - \alpha } \right\rangle - \left| { - \alpha ,\alpha } \right\rangle )$ field. When the parameter $\alpha $ is very large, the dynamic behaviours of $C_{\rm AB}$ are almost the same for the separable state, entangled coherent state $\left| u \right\rangle $ and $\left| {u}' \right\rangle $ fields. For the two-mode squeezed vacuum state field the maximum of $C_{\rm AB}$ increases monotonically with the squeezing parameter $r$, and as $r \to \infty $, $C_{\rm AB} \to 1$. This means that the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.

Internal Josephson-like tunnelling in two-component Bose--Einstein condensates affected by sign of the atomic interaction and external trapping potential

Xiong Bo, Liu Xun-Xu
Chin. Phys., 2007, 16 (9): 2578-2583 doi: 10.1088/1009-1963/16/9/013
Full Text: [PDF 737 KB] (Downloads:390)
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This paper studies the Josephson-like tunnelling in two-component Bose--Einstein condensates coupled with microwave field, which is in respond to various attractive and repulsive atomic interaction under the various aspect ratio of trapping potential. It is very interesting to find that the dynamic of Josephson-like tunnelling can be controlled from fast damped oscillations to nondamped oscillation, and relative number of atoms changes from asymmetric occupation to symmetric occupation correspondingly.

Realistic teleportation of coherent states using squeezed vacuum states

Yan Wei, Zhang Wei-Jun
Chin. Phys., 2007, 16 (9): 2584-2586 doi: 10.1088/1009-1963/16/9/014
Full Text: [PDF 86 KB] (Downloads:416)
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This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.

Dynamics of network motifs in genetic regulatory networks

Li Ying, Liu Zeng-Rong, Zhang Jian-Bao
Chin. Phys., 2007, 16 (9): 2587-2594 doi: 10.1088/1009-1963/16/9/015
Full Text: [PDF 472 KB] (Downloads:433)
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Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

Ning Li-Juan, Xu Wei, Yao Ming-Li
Chin. Phys., 2007, 16 (9): 2595-2599 doi: 10.1088/1009-1963/16/9/016
Full Text: [PDF 225 KB] (Downloads:483)
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In this paper the stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio (SNR) is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.

Quasispecies distribution of Eigen model

Chen Jia, Li Sheng, Ma Hong-Ru
Chin. Phys., 2007, 16 (9): 2600-2607 doi: 10.1088/1009-1963/16/9/017
Full Text: [PDF 704 KB] (Downloads:444)
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We have studied sharp peak landscapes of the Eigen model from a new perspective about how the quasispecies are distributed in the sequence space. To analyse the distribution more carefully, we bring in two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can gain a visual and in-depth result about how the sequences are distributed. We find that there are several local similarity optima around the centre (global similarity optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears to be linear near the threshold.

Generalized synchronization of two different chaotic systems

Li Guo-Hui
Chin. Phys., 2007, 16 (9): 2608-2611 doi: 10.1088/1009-1963/16/9/018
Full Text: [PDF 105 KB] (Downloads:598)
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In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a function relation. Based on rigorous analysis, the error system is asymptotically stable at the equilibrium. Numerical simulations illustrate the effectiveness of the proposed theory.

Projective synchronization in coupled fractional order chaotic Rossler system and its control

Shao Shi-Quan, Gao Xin, Liu Xing-Wen
Chin. Phys., 2007, 16 (9): 2612-2615 doi: 10.1088/1009-1963/16/9/019
Full Text: [PDF 312 KB] (Downloads:721)
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This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system's corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.

Generation of on--off intermittency based on R?ssler chaotic system

Zhou Qian, Chen Zeng-Qiang, Yuan Zhu-Zhi
Chin. Phys., 2007, 16 (9): 2616-2626 doi: 10.1088/1009-1963/16/9/020
Full Text: [PDF 4794 KB] (Downloads:486)
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In this paper, one-state on--off intermittency and two-state on--off intermittency are generated in two five-dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the R\"{o}ssler chaotic system. The parameter conditions under which the on--off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of $-3/2$, which is a signature of on--off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on--off intermittency based on a chaotic system, which is important for application and theoretical study.

Adaptive tracking control for a class of uncertain chaotic systems

Chen Feng-Xiang, Wang Wei, Zhang Wei-Dong
Chin. Phys., 2007, 16 (9): 2627-2630 doi: 10.1088/1009-1963/16/9/021
Full Text: [PDF 184 KB] (Downloads:472)
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The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.

Chaotic phenomena in Josephson circuits coupled quantum cellular neural networks

Wang Sen, Cai Li, Li Qin, Wu Gang
Chin. Phys., 2007, 16 (9): 2631-2634 doi: 10.1088/1009-1963/16/9/022
Full Text: [PDF 592 KB] (Downloads:537)
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In this paper the nonlinear dynamical behaviour of a quantum cellular neural network (QCNN) by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.

Canards in a rheodynamic model of cardiac pressure pulsations

Xie Feng, Chen Xian-Feng
Chin. Phys., 2007, 16 (9): 2635-2639 doi: 10.1088/1009-1963/16/9/023
Full Text: [PDF 217 KB] (Downloads:332)
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This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. The physiological significance of canards in this model is given.

Controlling spiral wave with target wave in oscillatory systems

Liu Fu-Cheng, Wang Xiao-Fei, Li Xue-Chen, Dong Li-Fang
Chin. Phys., 2007, 16 (9): 2640-2643 doi: 10.1088/1009-1963/16/9/024
Full Text: [PDF 809 KB] (Downloads:458)
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Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied.

Bifurcation phenomena of photodetached electron flux in parallel external fields

Gao Song, Li Hong-Yun, Yang Guang-Can, Lin Sheng-Lu
Chin. Phys., 2007, 16 (9): 2644-2649 doi: 10.1088/1009-1963/16/9/025
Full Text: [PDF 770 KB] (Downloads:391)
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A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H$^- $ in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions. We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.

Potential energy surfaces of ozone in the ground state

Shao Ju-Xiang, Zhu Zheng-He, Huang Duo-Hui, Wang Jun, Cheng Xin-Lu, Yang Xiang-Dong
Chin. Phys., 2007, 16 (9): 2650-2655 doi: 10.1088/1009-1963/16/9/026
Full Text: [PDF 324 KB] (Downloads:519)
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Equilibrium parameters of ozone, such as equilibrium geometry structure parameters, force constants and dissociation energy are presented by CBS-Q {\it ab initio} calculations. The calculated equilibrium geometry structure parameters and energy are in agreement with the corresponding experimental values. The potential energy function of ozone with a C$_{\rm 2v}$ symmetry in the ground state is described by the simplified Sorbie--Murrell many-body expansion potential function according to the ozone molecule symmetry. The contour of bond stretching vibration potential of an O$_{3}$ in the ground state, with a bond angle ($\theta )$ fixed, and the contour of O$_{3}$ potential for O rotating around O$_{1}$--O ($R_{1})$, with O$_{1}$--O bond length taken as the one at equilibrium, are plotted. Moreover, the potentials are analysed.

Tunnelling cooling by a normal--vacuum--superconductor junction

Zhang Xin, Zhang Dian-Lin
Chin. Phys., 2007, 16 (9): 2656-2660 doi: 10.1088/1009-1963/16/9/027
Full Text: [PDF 239 KB] (Downloads:374)
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The possibility of cooling a system from liquid helium temperature, 4.2~K, using a tunnel junction refrigerator is analysed. Calculations show that the device can be used over a wide temperature range from 4~K down to well below 1~mK with necessary cooling power. However, several serious difficulties must be overcome before the method can be used in low temperature laboratories.

Formation and local electronic structure of Ge clusters on Si(111)-7×7 surfaces

Ma Hai-Feng, Xu Ming-Chun, Yang Bing, Shi Dong-Xia, Guo Hai-Ming, Pang Shi-Jin, Gao Hong-Jun
Chin. Phys., 2007, 16 (9): 2661-2664 doi: 10.1088/1009-1963/16/9/028
Full Text: [PDF 1118 KB] (Downloads:384)
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We report the formation and local electronic structure of Ge clusters on the Si(111)-7$\times $7 surface studied by using variable temperature scanning tunnelling microscopy (VT-STM) and low-temperature scanning tunnelling spectroscopy (STS). Atom-resolved STM images reveal that the Ge atoms are prone to forming clusters with 1.0~nm in diameter for coverage up to 0.12~ML. Such Ge clusters preferentially nucleate at the centre of the faulted-half unit cells, leading to the `dark sites' of Si centre adatoms from the surrounding three unfaulted-half unit cells in filled-state images. Bias-dependent STM images show the charge transfer from the neighbouring Si adatoms to Ge clusters. Low-temperature STS of the Ge clusters reveals that there is a band gap on the Ge cluster and the large voltage threshold is about 0.9~V.
NUCLEAR PHYSICS

Effect of strong magnetic field on electron capture of iron group nuclei in crusts of neutron stars

Liu Jing-Jing, Luo Zhi-Quan, Liu Hong-Lin, Lai Xiang-Jun
Chin. Phys., 2007, 16 (9): 2671-2675 doi: 10.1088/1009-1963/16/9/030
Full Text: [PDF 857 KB] (Downloads:983)
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In this paper electron capture on iron group nuclei in crusts of neutron stars in a strong magnetic field is investigated. The results show that the magnetic fields have only a slight effect on electron capture rates in a range of 10$^{8}-10^{13}$G on surfaces of most neutron stars, whereas for some magnetars the magnetic fields range from 10$^{13}$ to 10$^{18}$~G. The electron capture rates of most iron group nuclei are greatly decreased, reduced by even four orders of magnitude due to the strong magnetic field.

Scaling of anisotropic flows and nuclear equation of state in intermediate energy heavy ion collisions

Yan Ting-Zhi, Ma Yu-Gang, Cai Xiang-Zhou, Fang De-Qing, Guo Wei, Ma Chun-Wang, Shen Wen-Qing, Tian Wen-Dong, Wang Kun
Chin. Phys., 2007, 16 (9): 2676-2682 doi: 10.1088/1009-1963/16/9/031
Full Text: [PDF 1090 KB] (Downloads:448)
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Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light clusters have been studied in detail for 25 MeV/nucleon $^{86}$Kr + $^{124}$Sn at large impact parameters by using a quantum molecular dynamics model with different potential parameters. Four sets of parameters including soft or hard equation of state (EOS) with or without symmetry energy term are used. Both number-of-nucleon ($A$) scaling of the elliptic flow versus transverse momentum ($p_{\rm t}$) and the scaling of $v_4/A^{2}$ versus $(p_{\rm t}/A)^2$ have been demonstrated for the light clusters in all above calculation conditions. It is also found that the ratio of $v_4/{v_2}^2$ maintains a constant of 1/2 which is independent of $p_{\rm t}$ for all the light fragments. Comparisons among different combinations of the EOS and the symmetry potential term show that the above scaling behaviours are sound and independent of the details of potential, while the strengths of flows are sensitive to the EOS and the symmetry potential term.

Evidence of intermittent fluctuation of target fragments in 84Kr--AgBr interactions at 1.7 A GeV

Zhang Dong-Hai, Li Xue-Qin, Jia Hui-Ming, He Chun-Le, Liu Fang, Zhao Hui-Hua, Li Zhen-Yu, Li Jun-Sheng
Chin. Phys., 2007, 16 (9): 2683-2688 doi: 10.1088/1009-1963/16/9/032
Full Text: [PDF 457 KB] (Downloads:457)
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Intermittency and fractal behaviour have been studied of emission spectra of target associated fragments from $^{84}$Kr--AgBr interactions at 1.7\,A GeV in emission angle space and azimuthal angle space separately. The intermittent behaviour is observed in the two spaces separately. From the intermittency exponent, the anomalous fractal dimension $d_{q}$ is calculated and the variation of $d_{q}$ with the order $q$ is investigated. It is found that the anomalous dimensions are found to increase with the order of moments $q$, thereby indicating the relation of multifractality to production mechanism of target associated fragments.

Intermittency in 3.7 A GeV 16O-emulsion interactions

Zhang Dong-Hai, Zhao Hui-Hua, Liu Fang, He Chun-Le, Jia Hui-Ming, Li Xue-Qin, Li Zhen-Yu, Li Jun-Sheng
Chin. Phys., 2007, 16 (9): 2689-2700 doi: 10.1088/1009-1963/16/9/033
Full Text: [PDF 1034 KB] (Downloads:496)
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The intermittency effect has been studied for an interaction of 3.7 A GeV $^{16}$O with emulsion using the distributions of both the pseudorapidity intervals and the azimuthal angle intervals of the shower particles emitted in a central rapidity region. The scaled factorial moments, reduced scaled factorial moments and multifractal moments as functions of the bin size in pseudorapidity and in azimuthal angle have been calculated and have revealed the presence of an intermittent behaviour which may be due to the random cascading property of the reaction. The anomalous fractal dimension has been found to increase with the increase of rank of the moment.
CLASSICAL AREAS OF PHENOMENOLOGY

Analytical structure of Hermite Gaussian beam in far field

Zhou Guo-Quan, Chen Liang, Chu Xiu-Xiang
Chin. Phys., 2007, 16 (9): 2709-2715 doi: 10.1088/1009-1963/16/9/035
Full Text: [PDF 1386 KB] (Downloads:564)
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Based on the vectorial structure of electromagnetic beam and the method of stationary phase, the analytical structure of Hermite Gaussian beam in far field is presented. The structural energy flux distributions are also investigated in the far field. The structural pictures of some Hermite Gaussian beams are depicted in the far field. As the structure of Hermite Gaussian beam is dominated by the transverse mode numbers and the initial transverse Gaussian half width, it is more complex than that of Gaussian beam. The ratios of the structural energy fluxes to the whole energy flux are independent of the transverse mode numbers and the initial transverse Gaussian half width. The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\

Space-charge limiting currents for magnetically focused intense relativistic electron beams

Li Jian-Qing, Mo Yuan-Long
Chin. Phys., 2007, 16 (9): 2716-2720 doi: 10.1088/1009-1963/16/9/036
Full Text: [PDF 149 KB] (Downloads:371)
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The self-consistent differential equations, which describe a laminar-flow equilibrium state in a magnetically focused intense relativistic electron beam propagating inside a conducting waveguide, are presented. The canonical angular momentum, $p_{\theta }$, defined under the conditions at the source, uniquely determines the possible solutions of these equations. By numerically solving these equations, the space-charge limited current and the externally applied magnetic field are obtained in a solid beam and a hollow beam in two cases of $p_{\theta }=0$ (magnetically shielded source) and $p_{\theta }=$~const. (immersed source) separately. It is shown that the hollow beam is more beneficial to the propagation of the intense relativistic beam through a drift tube than the solid beam.

An exact solution to paraxial propagation of laser beams in longitudinal inhomogeneous plasmas

Zhou Bing-Ju, Huang Zheng, Liu Ming-Wei, Liu Xiao-Juan
Chin. Phys., 2007, 16 (9): 2721-2724 doi: 10.1088/1009-1963/16/9/037
Full Text: [PDF 128 KB] (Downloads:480)
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An exact, general solution for laser beams propagating in longitudinally inhomogeneous plasmas is obtained in the form of the diffraction integral. The Gaussian beam and the Hermite--Gaussian beam are taken for example. In the case of an increasing plasma density along the propagation distance, natural diffraction of the Gaussian beam is retarded. This retardance has a less effect on the central part of the Hermite--Gaussian beam while a considerable rise of the power in bucket (PIB) occurs in the surrounding part of the beam.

Orientation-enhanced nonlinear optical properties and phase-conjugate reflective system of a novel Azobenzene doped polymer film

Xie Ru-Sheng, Fan Wen-Bin, Lu Ming, Zhao You-Yuan
Chin. Phys., 2007, 16 (9): 2725-2730 doi: 10.1088/1009-1963/16/9/038
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This paper reports that the nonlinear refractive index of a novel organic optical storage film doped azo-diphenylamine polymer is measured by using the $Z$-scan technique. The nonlinear refractive index up to $3.7\times 10 ^{ - 6 }$~cm$^{2}$/W induced by thermo-optical effect is obtained. It indicates that the sample has excellent optical nonlinear properties. The physical mechanism of the great nonlinear optical effect is analysed and the optical conjugate characteristic is also discussed with degenerate four-wave-mixing. The phase conjugate wave diffracted from the formative refractive index grating in the sample is acquired and its equivalent reflectivity reaches about 22{\%}. On this basis, the reflective wave phase-conjugated mirror system was designed, and the image aberration experienced in propagation in the storage experiment is corrected by using the system.

Potential fields of merging and splitting filaments in air

Ma Yuan-Yuan, Lu Xin, Xi Ting-Ting, Hao Zuo-Qiang, Gong Qi-Huang, Zhang Jie
Chin. Phys., 2007, 16 (9): 2731-2736 doi: 10.1088/1009-1963/16/9/039
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Two interacting light filaments with different initial phases propagating in air are investigated numerically by using a ray tracing method. The evolution of the rays of a filament is governed by a potential field. During propagation, the two potential wells of the two filaments can merge into one or repel each other, depending on the initial phase difference between the two filaments. The study provides a simple description of the interacting filaments.

A method of designing photonic crystal grating slow-wave circuit for Ribbon--Beam microwave travelling wave amplifiers

Yin Hai-Rong, Gong Yu-Bin, Wei Yan-Yu, Gong Hua-Rong, Yue Ling-Na, Lu Zhi-Gang, Huang Min-Zhi, Wang Wen-Xiang
Chin. Phys., 2007, 16 (9): 2737-2744 doi: 10.1088/1009-1963/16/9/040
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A method of designing a photonic crystal grating slow-wave circuit in which the cylinders of the 2D photonic crystals dot on a cross-sectional plane is established by calculating the band structures of the 2D photonic crystals, and the eigenfrequency of the equivalent waveguide grating. For calculating the band structures, the eigenvalue equations of the photonic crystals in the system of photonic crystal grating slow-wave circuit are derived in a special polarization mode. Two examples are taken to show the method. The design result is validated by the scattering parameters of the same circuit. The result indicates that there exists no photonic band gap if the metal gratings do not extend into the photonic crystals; the design of the circuit without the metal gratings extending into the photonic crystals is less flexible than that with the metal gratings extending into the photonic crystals.

Noninvasive temperature estimation by detecting echo-strain change including thermal expansion

Ma Yong, Zhang Dong, Gong Xiu-Fen, Liu Xiao-Zhou, Ma Qing-Yu, Qiu Yuan-Yuan
Chin. Phys., 2007, 16 (9): 2745-2751 doi: 10.1088/1009-1963/16/9/041
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This article studies the feasibility of noninvasive temperature estimation by detecting echo-strain including thermal expansion in therapeutic ultrasound treatment. This technique evaluates distributions of echo-strain and temperature inside the tissue by detecting echo signals pre- and post-heating, in combination with the temperature dependence of sound speed and thermal expansion. In the computer simulation and experimental study, echo signals pre- and post-heating are acquired and then the temperature elevation is evaluated by correlation analysis. Results demonstrate that this technique can effectively extend the measured temperature range up to 75$^{\circ}$C with an accuracy of $\pm $2$\,^{\circ}$C.
ATOMIC AND MOLECULAR PHYSICS

Ab initio calculations on the a3+u state properties of dimer 7Li2

Shi De-Heng, Sun Jin-Feng, Zhu Zun-Lue, Liu Yu-Fang
Chin. Phys., 2007, 16 (9): 2701-2708 doi: 10.1088/1009-1963/16/9/034
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The comparison between single-point energy scanning (SPES) and geometry optimization (OPT) in determining the equilibrium geometry of the $a^{3}\Sigma ^{ + }_{\rm u}$ state for $^{7}$Li$_{2}$ is made at numerous basis sets such as 6-311++G(2df), cc-PVTZ, 6-311++G(2df,p), 6-311G(3df,3pd), 6-311++G(2df,2pd), D95(3df,3pd), 6-311++G, DGDZVP, 6-311++G(3df,2pd), 6-311G(2df,2pd), D95V++, CEP-121G, 6-311++G(d,p), 6-311++G(2df,pd) and 6-311++G(3df,3pd) in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction (SAC/SAC-CI) method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at these sets over a wide internuclear distance range from about 3.0$a_{0}$ to 37.0$a_{0}$, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at cc-PVTZ, the spectroscopic data ($T_{\rm e}$, $D_{\rm e}$, $D_{0}$, $\omega _{\rm e },\omega _{\rm e}\chi _{\rm e}$, $\alpha _{\rm e}$ and $B_{\rm e})$ are computed and they are 1.006 eV, 338.71~cm$^{ - 1}$, 307.12 cm$^{ - 1}$, 64.88 cm$^{ - 1}$, 3.41 cm$^{ - 1}$, 0.0187 cm$^{ - 1}$ and 0.279 cm$^{ - 1}$, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at $J$=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant ($B_{\upsilon })$ and six centrifugal distortion constants ($D_{\upsilon }$ $H_{\upsilon }$, $L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are calculated. The scattering length is calculated to be --27.138$a_{0}$, which is in good accord with the experimental data.
THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Lie symmetry algebra of one-dimensional nonconservative dynamical systems

Liu Cui-Mei, Wu Run-Heng, Fu Jing-Li
Chin. Phys., 2007, 16 (9): 2665-2670 doi: 10.1088/1009-1963/16/9/029
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Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1--1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

Influence of air pressure on mechanical effect of laser plasma shock wave

Zhang Yu-Zhu, Wang Guang-An, Zhu Jin-Rong, Shen Zhong-Hua, Ni Xiao-Wu, Lu Jian
Chin. Phys., 2007, 16 (9): 2752-2756 doi: 10.1088/1009-1963/16/9/042
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The influence of air pressure on mechanical effect of laser plasma shock wave in a vacuum chamber produced by a Nd:YAG laser has been studied. The laser pulses with pulse width of 10ns and pulse energy of about 320mJ at 1.06$\mu $m wavelength is focused on the aluminium target mounted on a ballistic pendulum, and the air pressure in the chamber changes from $2.8\times 10^{3}$ to 1.01$\times $10$^{5 }$Pa. The experimental results show that the impulse coupling coefficient changes as the air pressure and the distance of the target from focus change. The mechanical effects of the plasma shock wave on the target are analysed at different distances from focus and the air pressure.

A comparison among optical emission spectroscopic methods of determining electron temperature in low pressure argon plasmas

Niu Tian-Ye, Cao Jin-Xiang, Liu Lei, Liu Jin-Ying, Wang Yan, Wang Liang, Lv You
Chin. Phys., 2007, 16 (9): 2757-2763 doi: 10.1088/1009-1963/16/9/043
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In this article, four kinds of optical emission spectroscopic methods of determining electron temperature are used to investigate the relationship between electron temperature and pressure in the cylindrical plasmas of dc glow discharges at low pressures in laboratory by measuring the relative intensities of ArI lines at various pressures. These methods are developed respectively on the basis of the Fermi--Dirac model, corona model, and two kinds of electron collision cross section models according to the kinetic analysis. Their theoretical bases and the conditions to which they are applicable are reviewed, and their calculation results and fitting errors are compared with each other. The investigation has indicated that the electron temperatures obtained by the four methods become consistent with each other when the pressure increases in the low pressure argon plasmas.
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Formation mechanism of Ge nanocrystals embedded in SiO2 studied by fluorescence x-ray absorption fine structure

Yan Wen-Sheng, Li Zhong-Rui, Sun Zhi-Hu, Pan Zhi-Yun, Wei Shi-Qiang
Chin. Phys., 2007, 16 (9): 2764-2768 doi: 10.1088/1009-1963/16/9/044
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This paper reports that the Ge nanocrystals embedded in SiO$_{2}$ matrix are grown on Si(100) and quartz--glass substrates, and the formation mechanism is systematically studied by using fluorescence x-ray absorption fine structure (XAFS). It is found that the formation of Ge nanocrystals strongly depends on the properties of substrate materials. In the as-prepared samples with Ge molar content of 60{\%}, Ge atoms exist in amorphous Ge (about 36{\%}) and GeO$_{2 }$ (about 24{\%}) phases. At the annealing temperature of 1073 K, on the quartz--glass substrate Ge nanocrystals are generated from crystallization of amorphous Ge, rather than from the direct decomposition of GeO$_{2}$ in the as-deposited sample. However, on the Si(100) substrate, the Ge nanocrystals are generated partly from crystallization of amorphous Ge, and partly from GeO$_{2}$ phases through the permutation reaction with Si substrate. Quantitative analysis reveals that about 10{\%} of GeO$_{2}$ in the as-prepared sample are permuted with Si wafer to form Ge nanocrystals.

Synthesis and photoluminescence study on ZnO nano-particles

Li Xiang, Zhai Fei-Fei, Liu Ying, Cao Mao-Sheng, Wang Fu-Chi, Zhang Xi-Xiang
Chin. Phys., 2007, 16 (9): 2769-2772 doi: 10.1088/1009-1963/16/9/045
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A new technique, namely low pressure sputtering, has been developed to fabricate Zn nanoparticles, with a subsequent oxidation to synthesize ZnO nanoparticles in the ambient atmosphere at 500$\,^{\circ}$C. The synthesized ZnO nanoparticle has a size of 6--8~nm with a preferred orientation of $c$-axis. The produced ZnO nanoparticles have a good UV photoluminescence (PL) emission energy of 3.349 eV with a significant enhancement of donor--acceptor pair emission located at 3.305 eV which implies a number of donor and acceptor bounded excitons existing in the synthesized ZnO nano particles. The near band edge PL emission of the fabricated ZnO is dominated by the bounded excitons at 10~K.

Experimental study on radiation effects in floating gate read-only-memories and static random access memories

He Chao-Hui, Li Yong-Hong
Chin. Phys., 2007, 16 (9): 2773-2778 doi: 10.1088/1009-1963/16/9/046
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Radiation effects of the floating gate read-only-memory (FG ROM) and the static random access memory (SRAM) have been evaluated using the 14~MeV neutron and 31.9MeV proton beams and Co-60 $\gamma $-rays. The neutron fluence, when the first error occurs in the FG ROMs, is at least 5 orders of magnitude higher than that in the SRAMs, and the proton fluence, 4 orders of magnitude higher. The total dose threshold for Co-60 $\gamma $-ray irradiation is about 10$^{4}$~rad (Si) for both memories. The difference and similarity are attributed to the structure of the memory cells and the mechanism of radiation effects. It is concluded that the FG ROMs are more reliable as semiconductor memories for storing data than the SRAMs, when they are used in the satellites or space crafts exposed to high energy particle radiation.

Molecular dynamics simulation of thermodynamic properties of YAG

Chen Jun, Chen Dong-Quan, Zhang Jing-Lin
Chin. Phys., 2007, 16 (9): 2779-2785 doi: 10.1088/1009-1963/16/9/047
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In this paper we study the thermodynamic properties of Y$_{3}$Al$_{5}$O$_{12}$ (YAG) by using molecular dynamic method combined with two- and three-body potentials. The dependences of melting process, elastic constant and diffusion coefficient on temperature of crystal YAG are simulated and compared with the experimental results. Our results show that anion O has the biggest self-diffusivity and cation Y has the smallest self-diffusivity in a crystal YAG. The calculated diffusion activation energies of ions O, Al and Y are 282.55, 439.46, 469.71kJ/mol, respectively. Comparing with experimental creep activation energy of YAG confirms that cation Y can restrict the diffusional creep rate of crystal YAG.

GaN layers with different polarities prepared by radio frequency molecular beam epitaxy and characterized by Raman scattering

Zhong Fei, Li Xin-Hua, Qiu Kai, Yin Zhi-Jun, Ji Chang-Jian, Cao Xian-Cun, Han Qi-Feng, Chen Jia-Rong, Wang Yu-Qi
Chin. Phys., 2007, 16 (9): 2786-2790 doi: 10.1088/1009-1963/16/9/048
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GaN layers with different polarities have been prepared by radio-frequency molecular beam epitaxy (RF-MBE) and characterized by Raman scattering. Polarity control are realized by controlling Al/N flux ratio during high temperature AlN buffer growth. The Raman results illustrate that the N-polarity GaN films have frequency shifts at $A_{1}$(LO) mode because of their high carrier density; the forbidden $A_{1}$(TO) mode occurs for mixed-polarity GaN films due to the destroyed translation symmetry by inversion domain boundaries (IDBS); Raman spectra for Ga-polarity GaN films show that they have neither frequency shifts mode nor forbidden mode. These results indicate that Ga-polarity GaN films have a better quality, and they are in good agreement with the results obtained from the room temperature Hall mobility. The best values of Ga-polarity GaN films are 1042 cm$^{2}$/Vs with a carrier density of 1.0$\times $10$^{17}$~cm$^{ - 3}$.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Electronic structure and optical properties of In-doped SrTiO3 by density function theory

Zhang Zhi-Yong, Yun Jiang-Ni, Zhang Fu-Chun
Chin. Phys., 2007, 16 (9): 2791-2797 doi: 10.1088/1009-1963/16/9/049
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The effect of In doping on the electronic structure and optical properties of SrTiO$_{3}$ is investigated by the first-principles calculation of plane wave ultra-soft pseudo-potential based on the density function theory (DFT). The calculated results reveal that due to the hole doping, the Fermi level shifts into valence bands (VBs) for SrTi$_{1-x}$In$_{x}$O$_{3 }$ with $x=0.125$ and the system exhibits p-type degenerate semiconductor features. It is suggested according to the density of states (DOS) of SrTi$_{0.875}$In$_{0.125}$O$_{3}$ that the band structure of p-type SrTiO$_{3}$ can be described by a rigid band model. At the same time, the DOS shifts towards high energies and the optical band gap is broadened. The wide band gap, small transition probability and weak absorption due to the low partial density of states (PDOS) of impurity in the Fermi level result in the optical transparency of the film. The optical transmittance of In doped SrTiO$_{3}$ is higher than 85{\%} in a visible region, and the transmittance improves greatly. And the cut-off wavelength shifts into a blue-light region with the increase of In doping concentration.

Role of atomic transverse migration in growth of diamond-like carbon films

Ma Tian-Bao, Hu Yuan-Zhong, Wang Hui
Chin. Phys., 2007, 16 (9): 2798-2802 doi: 10.1088/1009-1963/16/9/050
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The growth of diamond-like carbon (DLC) films is studied using molecular dynamics simulations. The effect of impact angle on film structure is carefully studied, which shows that the transverse migration of the incident atoms is the main channel of film relaxation. A transverse-migration-induced film relaxation model is presented to elucidate the process of film relaxation which advances the original model of subplantation. The process of DLC film growth on a rough surface is also investigated, as well as the evolution of microstructure and surface morphology of the film. A preferential-to-homogeneous growth mode and a smoothing of the film are observed, which are due to the transverse migration of the incident atoms.

High density Al2O3/TaN-based metal--insulator-- metal capacitors in application to radio frequency integrated circuits

Ding Shi-Jin, Huang Yu-Jian, Huang Yue, Pan Shao-Hui, Zhang Wei, Wang Li-Kang
Chin. Phys., 2007, 16 (9): 2803-2808 doi: 10.1088/1009-1963/16/9/051
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Metal--insulator--metal (MIM) capacitors with atomic-layer-deposited Al$_{2}$O$_{3}$ dielectric and reactively sputtered TaN electrodes in application to radio frequency integrated circuits have been characterized electrically. The capacitors exhibit a high density of about 6.05\,fF/$\mu $m$^{2}$, a small leakage current of $4.8\times 10^{-8}$\,A/cm$^{2}$ at 3\,V, a high breakdown electric field of 8.61\,MV/cm as well as acceptable voltage coefficients of capacitance (VCCs) of 795\,ppm/V$^{2}$ and 268\,ppm/V at 1\,MHz. The observed properties should be attributed to high-quality Al$_{2}$O$_{3}$ film and chemically stable TaN electrodes. Further, a logarithmically linear relationship between quadratic VCC and frequency is observed due to the change of relaxation time with carrier mobility in the dielectric. The conduction mechanism in the high field ranges is dominated by the Poole--Frenkel emission, and the leakage current in the low field ranges is likely to be associated with trap-assisted tunnelling. Meanwhile, the Al$_{2}$O$_{3}$ dielectric presents charge trapping under low voltage stresses, and defect generation under high voltage stresses, and it has a hard-breakdown performance.

Theoretical analysis of ion kinetic energies and DLC film deposition by CH4+Ar (He) dielectric barrier discharge plasmas

Liu Yan-Hong, Zhang Jia-Liang, Ma Teng-Cai, Li Jian, Liu Dong-Ping
Chin. Phys., 2007, 16 (9): 2809-2813 doi: 10.1088/1009-1963/16/9/052
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The kinetic energy of ions in dielectric barrier discharge plasmas are analysed theoretically using the model of binary collisions between ions and gas molecules. Langevin equation for ions in other gases, Blanc law for ions in mixed gases, and the two-temperature model for ions at higher reduced field are used to determine the ion mobility. The kinetic energies of ions in CH$_{4}$\,+\,Ar(He) dielectric barrier discharge plasma at a fixed total gas pressure and various Ar (He) concentrations are calculated. It is found that with increasing Ar (He) concentration in CH$_{4}$\,+\,Ar (He) from 20{\%} to 83{\%}, the CH$_{4}^{ + }$ kinetic energy increases from 69.6 (43.9) to 92.1 (128.5)\,eV, while the Ar$^{ + }$ (He$^{ + })$ kinetic energy decreases from 97 (145.2) to 78.8 (75.5)\,eV. The increase of CH$_{4}^{ + }$ kinetic energy is responsible for the increase of hardness of diamond-like carbon films deposited by CH$_{4}$\,+\,Ar (He) dielectric barrier discharge without bias voltage over substrates.
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

Amplitude death in steadily forced chaotic systems

Feng Guo-Lin, He Wen-Ping
Chin. Phys., 2007, 16 (9): 2825-2829 doi: 10.1088/1009-1963/16/9/055
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Steady forcing can induce the amplitude death in chaotic systems, which generally exists in coupled dynamic systems. Using the Lorenz system as a typical example, this paper investigates the dynamic behaviours of the chaotic system with steady forcing numerically, and finds that amplitude death can occur as the strength of the steady forcing goes beyond a critical constant.

Quintessence models with an oscillating equation of state and their potentials

Zhao Wen
Chin. Phys., 2007, 16 (9): 2830-2836 doi: 10.1088/1009-1963/16/9/056
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In this paper, we investigate the quintessence models with an oscillating equation of state (EOS) and its potentials. From the constructed potentials, which have an EOS of $\omega_{\phi}=\omega_0+\omega_1\sin z$, we find that they are all the oscillating functions of the field $\phi$, and the oscillating amplitudes decrease (or increase) with $\phi$. From the evolutive equation of the field $\phi$, we find that this is caused by the expansion of the universe. This also makes it very difficult to build a model whose EOS oscillates forever. However one can build a model with EOS oscillating for a certain period of time. Then we discuss three quintessence models, which are the combinations of the invert power law functions and the oscillating functions of the field $\phi$. We find that they all follow the oscillating EOS.
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