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CN 11-1958/O4
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Beating oscillation of two-dimensional electrons gas in narrow gap dilute magnetic semiconductor
Zhu Bo, Gui Yong-Sheng, Qiu Zhi-Jun, Zhou Wen-Zheng, Yao Wei, Guo Shao-Ling, Chu Jun-Hao, Zhang Fu-Jia
Acta Physica Sinica, 2006, 55 (2): 790
Acta Physica Sinica  
  Acta Physica Sinica--2006, 55 (2)   Published: 15 February 2006
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CLASSICAL AREA OF PHENOMENOLOGY

Optical properties of a two-dimensional array of absorptive and dispersive medium under near-resonant excitation

Li Zhi-Yu, Zhou Jian-Ying
Acta Physica Sinica. 2006, 55 (2): 0677 doi: 10.7498/aps.55.677
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A two_dimensional array of resonant absorptive and dispersive medium is proposed. The transmission,reflection and absorption spectra of optical field transmitting in the structure are calculated. The photonic band gap caused by resonance(PBG), similar as the case of one_dimensional active photonic crystal, is observed. It’s found that the resonance between the border of the Brillouin zone and the resonant center of the atom in the array is the key condition for the formation of the PBG. Further discussion is carried on the study of the dependence of transmission spectrum on the structure,the resonant center and the absorption linewidth of the atoms in the array.

Absorption and scattering of light by ice-water mixed clouds

Sun Xian-Ming, Han Yi-Ping
Acta Physica Sinica. 2006, 55 (2): 0682 doi: 10.7498/aps.55.682
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Based on the Mie theory,the light scattering properties in the visible regions of clouds consisting of pure water, pure ice spheres and concentric water_ice spheres are computed respectively. The reflection function and plane albedo, transmissivity, absorptivity of the three types of clouds are evaluated with the adding_doubling method by solving the radiative transfer equation. The numerical results show that the reflection function and plane albedo of ice clouds and ice_water clouds are slightly less than those of water clouds at most scattering angles, when the transmissivity is larger. A detailed theoretical analysis of the numerical results is presented, which explains the phenomenon of cloud absorption anomaly.

Fabrication of photonic crystals with different surface orientation by holographic lithography

Zhong Yong-Chun, Zhu Shao-An, Wang He-Zhou, Zeng Zhao-Hua, Chen Yong-Lie
Acta Physica Sinica. 2006, 55 (2): 0688 doi: 10.7498/aps.55.688
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A diamond_like structure, which has a large complete photonic band gap and needs only a low refractive index contrast to open the complete photonic band gap, have been fabricated using four umbrellalike beams. By use of special prism to match the beams, diamond_like crystals with special surface orientations have been fabricated. The capability and feasibility of this method have been demonstrated by the fabrication of long_range ordered diamond_like microstructures with (114) and (110) surface orientation. The fabrication of large crystals with adjustable surface orientations will be advantageous to the systematic investigation of photonic properties such as negative reflection etc.

Cubic model of a single-mode laser driven by quadratic pump noise and the steady probability distribution of laser intensity

Xu De-Sheng, Cao Li, Wu Da-Jin
Acta Physica Sinica. 2006, 55 (2): 0692 doi: 10.7498/aps.55.692
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A single_mode laser cubic model driven with quadratic pump noise is proposed. Closed laser intensity Langevin equation is got. Based on our early work of the Approximation Fokker_Planck equation (AFPE) for the systems driven by nonlinear external noise [Cao L and Wu D J 1988 Phys. Lett. A 133 476], the AFPE for laser intensity probability distribution is obtained. Exact analytic expression for the steady normalized intensity probability distribution is calculated. Based on the symmetry of steady normalized intensity probability distribution with respect to λ, the cross_correlation coefficient between the real and imaginary parts of pump noise, several general conclusions on the steady statistical property of laser system are reached.

Spontaneous emission from a Λ-type atom in anisotropic photonic crystal

Huang Xian-Shan, Xie Shuang-Yuan, Yang Ya-Ping
Acta Physica Sinica. 2006, 55 (2): 0696 doi: 10.7498/aps.55.696
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The spontaneous emission properties of a Λ_type atom embedded in anisotropic photonic crystals are investigated. We find that the dynamical properties of the atom and the propagating characteristics of the radiation field are obviously influenced by the relative position of the upper level from the forbidden gap and the space between the two lower levels. With the help of numerical calculation and theoretical analysis, we plot the evolution of the total radiation field and its components with the time. Furthermore, we also study the influence of photonic crystals on radiative properties of the atom by means of spontaneous emission spectrum.

Information entropy squeezing of the atom of an arbitrary initial state via the two-photon process

Liu Xiao-Juan, Zhou Bing-Ju, Fang Mao-Fa, Zhou Qing-Ping
Acta Physica Sinica. 2006, 55 (2): 0704 doi: 10.7498/aps.55.704
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From the quantum information point of view we investigate the entropy squeezing properties of a two_level atom with arbitrary initial state interacting with the coherent field via the two_photon process. The influence of the initial state of the system on the atomic information entropy squeezing is discussed. The numerical results obtained from the uncertainly relation of quantum information entropy are compared with those obtained from the uncertainly relation of Heisenberg. It is shown that the number of squeezed component of the atomic dipole, squeezed frequency, squeezed amplitude and squeezed direction of the atomic information entropy squeezing can be controlled by choosing the initial atomic distribution angle, the atomic mixing degree and the relative phase of the field mode, respectively. Quantum information entropy is a remarkable precise measure for the atomic squeezing.

Coherent-mode representation of the elegant Hermite-Gaussian beams

Dan You-Quan, Zhang Bin
Acta Physica Sinica. 2006, 55 (2): 0712 doi: 10.7498/aps.55.712
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Based on the theory of coherent_mode decomposition of laser beams, the mode correlation and coherent_mode representation of the elegant Hermite_Gaussian (EHG) beams are discussed. The analytical expressions for the mode coherence coefficients (MCCs) of EHG beams, which include a coherent_mode representation that consists of finite coherent_modes, are derived. Furthermore, the difference of the M2_factor between the EHG beams and SHG beams is analyzed by means of the mode structure of the EHG beams.

Numerical research of flat wideband supercontinuum generation in anomalous dispersion-flattened fibers

Chen Yong-Zhu, Li Yu-Zhong, Qu Gui, Xu Wen-Cheng
Acta Physica Sinica. 2006, 55 (2): 0717 doi: 10.7498/aps.55.717
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Supercontinuum generation in anomalous dispersion_flattened fibers through higher_order soliton compression effect is simulated and analyzed in detail. The results show that the second order differential constant of the dispersion parameter, dispersion parameter of the fiber and the pulse width, and peak power of the pump pulse are crucial to flat wideband supercontinuum generation, and the fiber length should also be dissimilarly chosen. It further shows that supercontinuum generation in the fiber mainly results from the interaction of self_phase modulation and group_velocity dispersions, and the higher_order nonlinear effects can be ignored.

Ab initio study on the second-order nonlinear optical properties of some coumarin derivatives

Liang Xiao-Rui, Zhao Bo, Zhou Zhi-Hua
Acta Physica Sinica. 2006, 55 (2): 0723 doi: 10.7498/aps.55.723
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The molecular structure of a series of coumarin derivatives were optimized and their second_order nonlinear optical polarizabilities(β) were calculated by the restricted Hartree_Fock (RHF) ab initio level with the 6_31G basis set in Gamess package. The results include both the distribution of charges in the ground and the excitated state and β under the external field(λ=1064nm). It is revealed that this kind of compounds have fairly large second_order polarizabilities. Moreover, there is close relation between the best structures and the high values of β. So we consider that this series of compounds are worthy of being studied further.

Study on complete band-gap of a kind of compound lattices

Pan Jie-Yong, Liang Guan-Quan, Mao Wei-Dong, Wang He-Zhou
Acta Physica Sinica. 2006, 55 (2): 0729 doi: 10.7498/aps.55.729
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A broad complete photonic band_gap (larger than 18%) in compound square lattices, and both single and double absolute band gaps in compound triangular lattices are obtained by optimization of the structure parameter. The relationship curves between absolute band gaps and the structure parameter are demonstrated. The simulation results also show that the shifts of two sub_lattices affect the band_gap a little.

Spectral properties of fcc-like cylindrical colloidal crystals

Wei Zhong-Chao, Dai Qiao-Feng, Wang He-Zhou
Acta Physica Sinica. 2006, 55 (2): 0733 doi: 10.7498/aps.55.733
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Colloidal crystals are grown in capillaries. Experimental results demonstrate that these colloidal crystals are formed in a structure with cylindrical symmetry. The colloidal crystals are relatively stable. In all radial directions in the plan perpendicular to the axis of the capillary, the transmission spectra are the same and the wavelength of the band gaps are the longest. In other directions, the wavelength of the band gap is gradually blue shifted as the angle between light and axis of capillary decreases. This axial symmetry of band gap will have many potential applications.

Influence of carrier-envelope phase on synthesizing of fundamental and its second-harmonic pulses

Deng Yu-Qiang, Wang Qing-Yue, Wu Zu-Bin, Zhang Zhi-Gang
Acta Physica Sinica. 2006, 55 (2): 0737 doi: 10.7498/aps.55.737
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Ultrabroadband spectrum is necessary for generation of ultrafast laser pulses; however, the extent of broadening the spectrum by its own nonlinear effect, such as self_phase modulation or cross phase modulation etc., is always limited. An easy way to broaden the spectrum to an octave is synthesizing the spectrum of its second-harmonic and the spectrum of itself. In this paper, influence of carrier_envelope phase on the synthesizing of two laser pulses is studied.
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

Optical conductivity of decagonal quasicrystals

Qiu Sheng-De, Hu Cheng-Zheng, Wang Ai-Jun, Zhou Xiang
Acta Physica Sinica. 2006, 55 (2): 0743 doi: 10.7498/aps.55.743
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A disscussion is given of the optical conductivity of decagonal quasicrystals. With group theory it is proved that decagonal quasicrystals may have different optical conductivity in the periodic and quasiperiodic directions. The formula is derived for the optical conductivity. The optical conductivity of Al65Co17Cu18 is calculated using this formula. The calculated results basically agree with the experimental data.

Structural properties of ZnO: In thin films prepared by sol-gel spin-coating technique

Lan Wei, Liu Xue-Qin, Huang Chun-Ming, Tang Guo-Mei, Yang Yang, Wang Yin-Yue
Acta Physica Sinica. 2006, 55 (2): 0748 doi: 10.7498/aps.55.748
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ZnO∶In thin films with thickness varying in the 210—240nm range were prepared on quartz substrates by sol_gel spin_coating technique. The structural properties of these thin films (In/Zn=0, 1, 2, 3 and 5at%) were studied by grazing incidence X_ray diffraction, conventional X_ray diffraction, Fourier transform infrared spectroscopy, atomic force microscopy and photoluminescence. It is found that the ZnO∶In thin films are composed of the unstressed bulk layer packed up by large grains with (002) plane and the surface layer by small grains with (002) and (103) planes, and a proper In doping concentration can improve structural properties of ZnO thin films. The analytic results were further proved by grazing incidence X_ray diffraction at different incidence angles (α=1, 2, 3 and 5°).

Third-order nonlinear optical properties of hybrid films of biopolymer-CdSe/ZnS core-shell quantum dots

Ding Sha, Wang Xiao-Hui, Du Yu-Min, Wang Qu-Quan
Acta Physica Sinica. 2006, 55 (2): 0753 doi: 10.7498/aps.55.753
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Biopolymer_CdSe/ZnS core_shell quantum dot hybrid films were prepared using self_assembly technique. Compared with the absorbance spectrum, the photoluminescence excited by laser with λ=395nm has Stokes shift. The third_order nonlinear optical properties of biopolymer_CdSe/ZnS film were studied by Z_scan setup with femtosecond laser at 790nm. It is found that the nonlinear absorptive signal partially originates from Cde/ZnS quantum dots while the nonlinear refractive signal partially originates from biopolymer chitosan. The magnitudes of them are measured to be β=6.5×10-6cm/W and n2=1.5×10-10cm2/W, respectively.

Method to improve absorption measurement sensitivity of thin films with surface thermal lens technique

Fan Shu-Hai, He Hong-Bo, Shao Jian-Da, Fan Zheng-Xiu, Zhao Yuan-An
Acta Physica Sinica. 2006, 55 (2): 0758 doi: 10.7498/aps.55.758
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In order to improve the sensitivity of surface thermal lens(STL) absorption measurement, numerical simulations are performed based on STL diffraction theory. The optimization method for choosing proper instrument parameters, including the size and position of probe laser waist and the position of detecting fiber, is developed from the simulation. The sensitivity of the instrument reaches 0.1ppm after the optimization.

Many-body contributions to the equation of state for highly compressed solid helium

Tian Chun-Ling, Liu Fu-Sheng, Cai Ling-Cang, Jing Fu-Qian
Acta Physica Sinica. 2006, 55 (2): 0764 doi: 10.7498/aps.55.764
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To investigate the significance of various many_body effects on the equation of state (EOS) of solid helium,the interaction energy of hcp crystal structure is expanded as a sum of two_ to five_body potentials in the present work. Each short_range many_body term between helium atom clusters is computed by means of Hartree_Fock (HF) self_consistent_field (SCF) method. It is indicated that at high densities the many_body expansion formula is an alternative series, in which two_, and four_body terms are positive, whereas three_ and five_body terms are negative. According to such an expansion of crystal interaction energy, the equation of state of solid helium at 0 K is obtained. The specific characteristics of each of the up to five_body contributions in highly compressed helium are discussed. Between 0.26 to 0.23nm, the interaction energy may be well described by two_ and three_body interactions. Over a distance range 0.23—0.20nm, truncated many_body expansion after the four_body term recovers the main part of atomic potential energy. Below 0.20nm the five_body contributions have to be included. The sum of two_ to five_body term accurately reproduces the atomic potential energy from 0.20 to 0.175nm. The inclusion up to five_body potential satisfactorily describes the available experimental data from 7.5 to 2.5 cm3/mol, corresponding to 1—60 GPa.

Epitaxial growth and superhardness effect in TiN/Al2O3 nanomultilayers

Kong Ming, Wei Lun, Dong Yun-Shan, Li Ge-Yang
Acta Physica Sinica. 2006, 55 (2): 0770 doi: 10.7498/aps.55.770
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TiN/Al2O3 nanomultilayers with various Al2O3 layer thicknesses were prepared by multi_target magnetron sputtering. The chemical composition, microstructure and mechanical properties of these multilayers were characterized by energy dispersive X_ray spectrometry, X_ray diffraction, high_resolution transmission electron microscopy and nanoindentation. The result raveals that under the sputtering conditions, normally amorphous Al2O3 is forced to crystallize at very small layer thicknesses (<1.5 nm), and grows coherently and epitaxially over TiN layers. Correspondingly, the hardness of the multilayers increases significantly and reaches a maximum value of 37.9 GPa. Further increasing in layer thickness, Al2O3 layers form an amorphous structure and block the coherent growth of the multilayers, and thus the hardness decreases gradually.
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Ordering and interaction of Fe and RE atoms on grain boundaries in ZA27 alloys

Liu Gui-Li, Li Rong-De
Acta Physica Sinica. 2006, 55 (2): 0776 doi: 10.7498/aps.55.776
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In order to reveal the behaviors of Fe and RE atoms on grain boundaries in ZA27 alloy theoretically, the atomic structure model of high angle grain boundary of α phase in ZA27 alloy was set up by using the concept of coincidence-site lattice(CSL). The electronic structure (state density, Fermi energy level, structure energy) of grain boundary was calculated using the recursion method. The clustering energy of alloying atoms was defined by the structure energy of grain boundary, and the clustering energies of Fe or RE atoms on grain boundary was calculated. The calculated results show that: the clustering energy of Fe or RE atoms gathered on grain boundary in ZA27 alloys is positive, so they can not form clusters and have the ordering tendency. Fe and RE atoms prefer to form steady inter_metallic compounds, and can form the negative electricity center on grain boundary in ZA27 alloys, thus reducing the Fermi energy level of grain boundary.

Simulation of multiple grains for isothermal solidification of binary alloy using phase-field model

Lu Yang, Wang Fan, Zhu Chang-Sheng, Wang Zhi-Ping
Acta Physica Sinica. 2006, 55 (2): 0780 doi: 10.7498/aps.55.780
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The phase-field model based on Kim model which couples the solute field is used to simulate microstructural dendrite growth of multiple grains for Al-2-mole-Cu alloy. In order to improve the efficiency of calculation, an interpolative method is used to achieve the coupling of the macro field with the micro field. The influence of different undercooling on shapes of dendrites and distribution of solute is studied.The result shows that the re-distribution of solute can decrease the melting point of the alloy, and reduce the practical undercooling, so the constitutional supercooling can influence the growth rate and solute distribution of dendrites by decreasing the freezing point evidently, and at the same time results in the cease of growth for both collided dendrites and perferred growth in directions of unhindered grains.

Beating oscillation of two-dimensional electrons gas in narrow gap dilute magnetic semiconductor Hot!

Zhu Bo, Gui Yong-Sheng, Qiu Zhi-Jun, Zhou Wen-Zheng, Yao Wei, Guo Shao-Ling, Chu Jun-Hao, Zhang Fu-Jia
Acta Physica Sinica. 2006, 55 (2): 0786 doi: 10.7498/aps.55.786
Full Text: [PDF 237 KB] Download:(1177)
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This paper studies the detailed beating oscillation in Shubnikov-de Hass (SdH) of magnetic two dimensional electron gas consisting of a modulation doped n type Hg0.82Cd0.16Mn0.02Te/Hg0.3Cd0.7Te first type quantum well, by which found that temperature, gate voltage are both bring the variety of magnetic resistance beating node position. By analyzing beating patterns, gate voltage dependent Rashba spin-orbit splitting can be separated from temperature dependent giant Zeeman splitting.

Linear Stark effect of CdS/HgS/CdS spherical nanometric system

Zheng Rui-Lun, Wen Guo-Zhi
Acta Physica Sinica. 2006, 55 (2): 0791 doi: 10.7498/aps.55.791
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Electronic energy and wave function of three-layer spherical nanometric system in homogeneous electric field is solved, the influence of applied field and sample size to the shift of Stark energy level is discussed.

Calculation of field enhancement factor of the carbon nanotube array

Wang Miao, Shang Xue-Fu, Li Zhen-Hua, Wang Xin-Qing, Xu Ya-Bo
Acta Physica Sinica. 2006, 55 (2): 0797 doi: 10.7498/aps.55.797
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To estimate the apex field enhancement factor associated with an array of carbon nanotubes (CNTs) on a planar cathode surface, the model of floating spheres between parallel anode and cathode plates is proposed. An approximate formula for the enhancement factor is derived, showing that the intertube distance of a CNT array critically affects the field emission. When the intertube distance is less than the height of the tube, the enhancement factor decreases rapidly with decreasing distance, qualitatively in agreement with the numerical simulation. Considering the field emission current density, the field emission can be optimized when the intertube distance is comparable with the tube height, in accordance with the results from experiments. Finally, the influence of the anode-cathode distance on the enhancement factor is also discussed, showing that the anode-cathode distance has little effect on the field emission from CNT array. Thus, we can reduce the threshold voltage to some extent by decreasing the anode-cathode distance.

Chemical surface treatment and charge stability of polypropylene cellular electret film

An Zhen-Lian, Tang Min-Min, Xia Zhong-Fu, Sheng Xiao-Chen, Zhang Xiao-Qing
Acta Physica Sinica. 2006, 55 (2): 0803 doi: 10.7498/aps.55.803
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The charge stability has been systematically studied by measuring open-circuit thermally stimulated discharge (TSD) current spectra, in situ TSD charge spectra and isothermal charge decay for the polypropylene (PP) cellular films after chemical treatments ( extraction, oxidation and HF solution treatment). The results showed that a very strong new current peak, which the virginal film does not have, appeared at about 184℃ in the TSD current spectrum of the PP cellular film properly oxidized and then HF-treated at room temperature (RT), and that its charge storage thermal stability is significantly improved compared with that of the virginal PP film, and is enhanced further by high temperature charging method. The reason that charge stability of the HF-treated PP films is improved has been clarified by attenuated total reflection infrared (ATR-IR) spectroscopy. The charge stability of treated films can be improved by appropriately prolonging either HF treatment time at RT or oxidation time. The theory of in situ TSD charge indicates that an in situ TSD charge spectrum contains combined information on the changes of the mean charge depth of the deposited charge layer and the deposited charge value. Combining the TSD current spectrum and the initial mean charge depth of a PP cellular film at RT, the change of the mean charge depth can be in situ investigated in heating process.

Influence of TbDyFe film on giant magnetoimpedance in sandwiched films

Shao Ming-Hui, Chen Qing-Yong, Zheng Wu
Acta Physica Sinica. 2006, 55 (2): 0811 doi: 10.7498/aps.55.811
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The Ni80.2Fe14.1Si0.2Mn0.4Mo5.1 sandwiched films are prepared on the magnetostrictive (Tb0.27Dy0.73)0.3Fe0.7 film substrate. Due to magnetostrictive stress effect on magnetic anisotropy which is believed to be critical for the giant magneto-impedance (GMI) effect, the GMI ratio is seen to increase sharply in the magnetic fields. The GMI effect also increases when the samples are annealed at 280℃. But the GMI ratio is still less than that of the as-deposited films.

Quantum effect of dissipative mesoscopic capacitance coupled circuit

Qiu Shen-Yu, Cai Shao-Hong
Acta Physica Sinica. 2006, 55 (2): 0816 doi: 10.7498/aps.55.816
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The dissipative mesoscopic coupled circuits are obtained by the method of damped harmonic oscillator quantization . The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given .The result shows that the quantum fluctuations of the charge and current exist in all states, and the fluctuations in the component circuits are corelated.

Mechanism of NBTI degradation in ultra deep submicron PMOSFET’s

Li Zhong-He, Liu Hong-Xia, Hao Yue
Acta Physica Sinica. 2006, 55 (2): 0820 doi: 10.7498/aps.55.820
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The mechanism of negative bias temperature instability (NBTI) degradation in ultra deep submicron PMOSFET's is investigated. We mainly focus on the threshold voltage shift under subsequent positive bias temperature (PBT) stress after the preceding NBT. It's experimentally demonstrated that trapped holes from inversion channel and the diffusion of hydrogen molecules in the gate oxide are the major causes of NBTI degradation in PMOSFET's. When the condition is switched to PBT stress the trapped holes can be rapidly detrapped, but only a part of hydrogen molecules can diffuse back to the interface of gate oxide and substrate and repassivate silicon dangling bond, this is responsible for the threshold voltage being only partially recovered during PBT annealing.

The research on metal induced crystallization with chemical source

Zhao Shu-Yun, Wu Chun-Ya, Li Juan, Liu Jian-Ping, Zhang Xiao-Dan, Zhang Li-Zhu, Meng Zhi-Guo, Xiong Shao-Zhen
Acta Physica Sinica. 2006, 55 (2): 0825 doi: 10.7498/aps.55.825
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The metal induced crystallization with chemical source on different silicon based films is studied. All amorphous silicon films deposited by LPCVD, RF-PECVD and VHF-PECVD have been crystallized. However, the a-Si films prepared by VHF-PECVD seems to have crystallized better. The crystallization was also affected by the concentration of the chemical solution. Under a certain conditions, the polycrystalline silicon crystallized with the solution of 10000ppm has larger grain size than that with 5000ppm solution. The annealing atmosphere also affects the crystallization process. Compared with the physical inducing source, the chemical inducing source gives different micro-crystallization structures. For the metal induced crystallization, the chemical source tends to be more advantageous.

Study of current in superconductive rings

Liang Fang-Ying, Li Han-Ming, Li Ying-Jun
Acta Physica Sinica. 2006, 55 (2): 0830 doi: 10.7498/aps.55.830
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We use a modified time-dependant Ginzburg-Landau model to study the characteristics of superconductive rings and evaluate the vortex motion equations. We show in theory that the flux has jumps, find sign reversal of the current and obtain expressions that are in accordance with the data of experiments.

Tunneling conductance anomalies in normal metal/triplet superconductor junction

Li Xiao-Wei, Liu Shu-Jing
Acta Physica Sinica. 2006, 55 (2): 0834 doi: 10.7498/aps.55.834
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In the framework of the Blonder-Tinkham-Klapwijk model,we calculate the differential tunneling conductance in normal metal / insulator / normal metal/triplet p-wave superconductor junctions which is studied theoretically as a function of the bias voltage. The results show that there are zero-bias conductance peak, zero-bias conductance dip, double-minimum structures and oscillation components of the differential conductance in the spectra for p-wave superconductor junctions. It can be seen that additional current steps appear in the I-V relationship. The existence of such structures in the conductance spectrum may serve as an evidence that the pairing of Sr2RuO4 has p-wave symmetry.

Two-step depinning and reentrant superconducting phase of moving vortex lattice in disordered superconductors

He Guo-Liang, He Yan-Wen, Zhao Zhi-Gang, Liu Mei
Acta Physica Sinica. 2006, 55 (2): 0839 doi: 10.7498/aps.55.839
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We developed a 3D flux_line lattice model with magnetic interactions between intraplane and interplane vortices to simulate the transport properties and the dynamic behavior of disordered anisotropic superconductors. We observed a double peak in the differential resistivity as the driving current increases, which corresponds to a two-step depinning in the vortex motion. Between the two peaks we also observed a reentering pinning phase. We also show that the transition from 2D plastic flow to 3D elastic flow of vortex motion is a recoupling transition which is associated with the double peak in differential resistivity. The increase of critical current of 3D-2D transition with the increasing of magnetic field (decreasing of relative interlayer coupling strength), indicates of a second peak effect.

Study on the superheating phenomenon of YBCO thin film

Cai Yan-Qing, Yao Xin, Li Gang
Acta Physica Sinica. 2006, 55 (2): 0844 doi: 10.7498/aps.55.844
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By using high temperature optical microscopy (HTOM), the superheating phenomenon in YBa2Cu3Oz (Y123) oxide thin film was found by in-situ observation of its melting process. The origin of superheating is discussed in combination with the analysis of XRD pole figure and the unwettability of Ba-Cu-O melts. Besides, the relationship between the microstructure of YBCO thin film and its superheating degree was investigated. The film with lower fraction of interface defects is believed to have higher superheating degree. The results deduced from semi-coherent interface energy theory are in good agreement with the experimental results of HTOM, AFM and XRD.

Influence of doping Al at Fe site on the magnetic structure and magnetotransport properties of Sr2FeMoO6

Wang Xian-Jie, Sui Yu, Qian Zheng-Nan, Liu Zhi-Guo, Miao Ji-Peng, Huang Xi-Qiang, Lü Zhe, Zhu Rui-Bin, Cheng Jin-Guang, Su Wen-Hui
Acta Physica Sinica. 2006, 55 (2): 0849 doi: 10.7498/aps.55.849
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Double perovskite Sr2FeMoO6 with Al doping at Fe site up to 30% were prepared by traditional solid-state reaction. The degree of the cation ordering of Sr2FeMoO6 increases with Al doping obviously as shown by the refinement of room-temperature X-ray diffraction. The saturated magnetic moment per formula unit of these compounds decreases gradually with increasing Al concentration, but the magnetic moment per Fe ion increases markedly, which is consistent with the improvement of cation ordering. Basing on the analysis of magnetic structure with Al doping, doping of Al will lead to the formation of non-magnetic coupled Mo—O—Al—O—Mo chains, which can divide the large Mo—O—Fe ferrimagnetic region into smaller patches and enhance the low field magnetoresistance. The formation of Fe—O—Fe antiphase boundaries are suppressed by the doping Al due to the improvement of the cation ordering, and the high field magnetoresistance that roots in spin-dependent scattering at the antiphase boundaries is reduced. Therefore, the total magnetoresistance reaches a maximum value at x=0.15.

Transport properties and magnetoresistance of nano-polycrystalline La0.7Sr0.3MnO3-δ

Xi Li, Yang Xiao-Lin, Li Cheng-Xian, Ge Shi-Hui
Acta Physica Sinica. 2006, 55 (2): 0854 doi: 10.7498/aps.55.854
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The resistivity and magnetoresistance of bulk polycrystalline La0.7Sr0.3MnO3-δ, fabricated to produce nanoscale grains sintered at different temperatures, have been investigated as functions of temperature. With decreasing temperature below room temperature the resistivity (ρ) exhibits a maximum near 250K, below which it shows “metallic" behaviour, i.e. ρ∝T2 in the temperature range from 50K to 170K. However, ρ subsequentlyexhibits a minimum near 50K, below which it is well fit by the predictions of the tunneling of conduction electrons through insulating interfacial layers, viz lnρ ∝T1/2, a result interpreted as conduction-electron tunneling between adjacent LSM granules. The minimum of ρ occuring in these samples may result from the competition of the tunneling effect and the intrinsic metallic transport mechanism of LSM. The temperature dependence of the associated tunneling magnetoresistance is also reported.

Perpendicular current-driven magnetization switching in free layer of magnetic tunneling junctions and MRAM

Peng Zi-Long, Han Xiu-Feng, Zhao Su-Fen, Wei Hong-Xiang, Du Guan-Xiang, Zhan Wen-Shan
Acta Physica Sinica. 2006, 55 (2): 0860 doi: 10.7498/aps.55.860
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A new method of readout and writing process driven by perpendicular current in magnetoresistantive random access memory (MRAM) based on the magnetic tunneling junction is reported, and its schematic structure and operation are described.

Influences of W doping at Mn site on magnetic structure of La0.3Ca0.7MnO3 system

Guo Huan-Yin, Liu Ning, Cai Zhi-Rang, Zhang Yu-Heng
Acta Physica Sinica. 2006, 55 (2): 0865 doi: 10.7498/aps.55.865
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The influences of W doping at Mn site on the magnetic structure of the charge-ordering system La0.3Ca0.7MnO3 are studied by the measurements of M_T curves,M_H curves and ESR spectra of polycrystalline samples of La0.3Ca0.7Mn1-xWxO3(x=0.00,0.04,0.08,0.12,0.15) are studied. The results show that when the doping amount is 0.00≤x≤0.08, the charge-ordering(CO) phase exists in the system, the AFM/CO states coexist below the transition temperature, and the charge-ordering temperature Tco goes up with the increase of W doping content. For the sample of x=0.04, FM phase and AFM/CO phases coexist at low temperature, and FM is separated from PM both before and after the formation of CO phase; when x≥0.12, CO state melts, and the paramagnetism-ferromagnetism (PM-FM) transition exists at extremely low temperature.

Electronic and magnetic properties of 3d transition-metal-doped Ⅲ-Ⅴ semiconductors:first-principle calculations

Lin Qiu-Bao, Li Ren-Quan, Zeng Yong-Zhi, Zhu Zi-Zhong
Acta Physica Sinica. 2006, 55 (2): 0873 doi: 10.7498/aps.55.873
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A systematic study based on ab initio calculations within the local spin density approximation (LSDA) has been performed on the Ⅲ-Ⅴ semiconductors (GaAs and GaP) doped by the 3d-transition metals (TM=V, Cr, Mn, Fe, Co and Ni). It is shown that the ferromagnetic (FM) state will be realized when the GaAs and GaP are doped by V, Cr or Mn, however, the system is antiferromagnetic (AFM) when doped by Fe; whereas these dilute magnetic semicondutors(DMS's) show unstable magnetism when doped by Co or Ni. It is suggested that Ⅲ-Ⅴ semiconductors doped by Cr can be candidates for high Curie Temperature DMS. For the present systems, the magnetic moment of V ion is greater than the theoretical value, those of Fe, Co and Ni are smaller than theoretical values, whereas for those of Cr and Mn, the difference between TM's magnetic moment and the expected value depends on the crystal symmetry and electronic states of ions. Finally, we show that, by the co-doping of Si and Mn in GaAs and GaP, the DMS's present a more stable FM state and a higher TC.

Structure, spin reorientation and M?ssbauer spectra of Tb0.3Dy0.7(Fe0.9T0.1)1.95 alloys

Zheng Xiao-Ping, Zhang Pei-Feng, Fan Duo-Wang, Li Fa-Shen, Hao Yuan
Acta Physica Sinica. 2006, 55 (2): 0879 doi: 10.7498/aps.55.879
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The effect of T substitution for Fe on the structure, spin reorientation and Mssbauer spectra of a series of Tb0.3Dy0.7(Fe0.9T0.1)1.95 (T=Mn,Fe,Co,B,Al,Ga) alloys at room temperature has been investigated systemically. The X-ray result shows that all samples are single phase having the cubic Laves-phase structure (C15). The analysis of the Mssbauer spectra indicates that the easy magnetization direction in the {110} plane deviates slightly from the main axis of symmetry for Al and Ga substitution, but remains in the [111] direction for B, Mn and Co substitution. The hyperfine field decreases slightly for Al and Ga substitution, does not change for B,Mn substitution and increases greatly for Co substitution. With the substitution of all elements but Co, the isomer shift and the quaduple splitting always increase.

Precise time integral of the Bloch equations and its application to the design of radio frequency pulses

Chen Jie-Fu, Liu Wan-Qiu, Zhong Wan-Xie
Acta Physica Sinica. 2006, 55 (2): 0884 doi: 10.7498/aps.55.884
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Solving the Bloch equations is a core procedure in the optimal design of radio frequency pulses, which has direct impacts on the quality of acquired images in magnetic resonance imaging. Although the analytical solutions of the Bloch equations exist under some circumstances, they hardly can be applied for practical use because of their complexity and lack of generality. In this paper, we employ precise time integration to solve the Bloch equations. Based on a high precision algorithm and in conjunction with a global optimization algorithm, we provide a complate procedure for the design of radio frequency pulses. The numerical data listed at the end of this paper demonstrate that the pulses derived from our algorithm have good frequency selectivity.

Ferromagnetic resonance study of Ni nanowire arrays

Yuan Shu-Juan, Zhou Shi-Ming, Lu Mu
Acta Physica Sinica. 2006, 55 (2): 0891 doi: 10.7498/aps.55.891
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Arrays of Ni nanowires were electrodeposited into anodic alumina oxide templates with various pore diameters and porosity. The magnetization behavior of the Ni nanowire arrays was investigated with ferromagnetic resonance techniques and the vibrating sample magnetometer. Both ferromagnetic resonance spectra and hysteresis loops show that there is a strong dipolar interaction between the nanowires. The easy axis of magnetization is mainly a result of a competition of shape anisotropy and dipolar interaction. With increasing array density, the dipolar interactions increase and the easy axis is tuned from parallel to perpendicular to the wire axis.

Ferromagnetic resonance in ferromagnetic/antiferromagnetic bilayers under the stress field

Pan Jing, Ma Mei, Zhou Lan, Hu Jing-Guo
Acta Physica Sinica. 2006, 55 (2): 0897 doi: 10.7498/aps.55.897
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Using a method based on the system energy described by Smith and Beljers, the ferromagnetic resonance in ferromagnetic (FM)/Antiferromagnetic (AFM) bilayers under the stress field is studied. The thin FM film is taken to be a single crystal with cubic and uniaxial magnetocrystalline anisotropies, while the thickness of AFM layer is thin enough for its energy to be neglected. Numerical calculations show that the stress field will affect resonance curve only under weak magnetic field, and the critical field strength which distinguishes the weak from the strong external field depends on the direction of the stress field only.

Influence of charging parameters on piezoelectricity for cellular PP film electrets

Zhang Peng-Feng, Xia Zhong-Fu, Qiu Xun-Lin, Wang Fei-Peng, Wu Xian-Yong
Acta Physica Sinica. 2006, 55 (2): 0904 doi: 10.7498/aps.55.904
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The influence of charging parameters (such as charging voltage, charging time and charging temperature, etc.) on piezoelectricity and its thermal stability of cellular polypropylene film electrets was studied by means of contact charging and constant voltage corona charging methods and the thermal stimulated discharge technique. The cause of the influence is discussed in connection with the structure and the theoretic model of the cellular piezoelectric film electrets, and its dynamic characteristic of space charge is also analyzed. The results show that the piezoelectricity and its thermal stability of these electrets may be improved by optimizing the charging parameters.It is hoped that this work will be helpful to widen the application of cellular PP and will offer theoretic and technical basis for its industrialization.

Analysis of the all-angle polarization beam splitting effect of the multi-layered wavy films

Li Yi-Yu, Gu Pei-Fu, Li Ming-Yu, Liu Xu, Yang Hui
Acta Physica Sinica. 2006, 55 (2): 0910 doi: 10.7498/aps.55.910
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The necessary conditions of all-angle polarization beam splitting effect of photonic crystal is discussed from the aspects of band structure and equal frequency surface. The conservation law of the tangential k-vector component is illustrated in the equal frequency surface. In order to theoretically verify the all-angle polarization beam splitting effect, finite-difference time-domain (FDTD) method is employed to simulate the propagation of Gauss beam in the multi-layered wavy films, getting the transmission coefficients for the TE and TM modes in the angle range from 8° to 89° respectively.

Micro-Raman scattering study of hexagonal InGaN epitaxial layer

Wang Rui-Min, Chen Guang-De, Zhu You-Zhang
Acta Physica Sinica. 2006, 55 (2): 0914 doi: 10.7498/aps.55.914
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Hexagonal InxGa1-xN film grown by metalorganic chemical vapor deposition (MOCVD) was studied by Micro-Raman scattering and X-ray diffraction. The phase separation was observed in InxGa1-xN, the biaxial stress was measured by both Raman and X-ray diffraction. In Raman spectroscopy, the A1(LO) mode of InxGa1-xN is absent. Instead, the LO phonon-plasmon coupled mode (LPP+) was observed at about 778 cm-1. The carrier concentration was determined by the frequency of the coupled mode. The E2 and A1(TO)modes of InxGa1-xN layer exhibit a down-shift compare to those of GaN layer. At low temperature, the peak induced by electronic transition was observed in Raman spectra of InxGa1-xN.

Random lasing in ZnO nanparticles

Chen Lei, Lou Qi-Hong, Wang Zhi-Jiang, Dong Jing-Xing, Wei Yun-Rong
Acta Physica Sinica. 2006, 55 (2): 0920 doi: 10.7498/aps.55.920
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In our experiment, the ZnO nanoparticles(diameter about 100nm) are optically pumped by the third harmonics (355 nm wavelength) of a pulsed Nd:YAG laser (30Hz repetition ration rate, 8ns pulse width). Laser-like light emission was observed in the ZnO nanoparticles. We simulate the ZnO particle density transport versus mean free path using the ring cavity theory. The result shows that random lasing can be produced in the ZnO particle with Nd:YAG (pulse width 8 ns).

Effect of introducing Ce3+ on the emission properties of Er3+/Yb3+-doped TeO2-WO3-ZnO glasses

Li Jia-Cheng, Xue Tian-Feng, Fan You-Yu, Li Shun-Guang, Hu He-Fang
Acta Physica Sinica. 2006, 55 (2): 0923 doi: 10.7498/aps.55.923
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Ce3+ ions were introduced into the Er3+/Yb3+-codoped TeO2-WO3-ZnO glasses, and the effect of Ce3+ on the emission properties at 1.5μm band and the upconversion luminescence of Er3+ in the glasses was investigated. With the increasing of Ce3+ concentration, the emission intensity of Er3+ at 1.5μm band increases firstly, and then decreases. The optimal doping concentration of Ce3+ is about 2.07×1020/cm3. As for the Er3+ emission at 1.5-μm band, the fluorescence lifetime decreases a little from 3.4ms to 3.0ms, while the full width at half maximum (FWHM) hardly changes with the increase of Ce3+ concentration. Due to the effective cross relaxation between Ce3+ and Er3+: Er3+(4I11/2)+Ce3+(2F5/2)→Er3+(4I13/2)+Ce3+(2F7/2), the upconversion emission intensity of Er3+ is reduced greatly. But when Ce3+-doping concentration is too high, the other cross relaxation between Ce3+ and Er3+: Er3+(4I13/2)+Ce3+(2F5/2)→Er3+(4I15/2)+Ce3+(2F7/2) happens, which depopulates the 4I13/2 level of Er3+ and results in the decrease of the emission intensity and fluorescence lifetime of Er3+ at 1.5μm band.

Influence of doping with titania nanotubes on performance of polymer light-emitting diodes

Qian Lei, Teng Feng, Xu Zheng, Quan Shan-Yu, Liu De-Ang, Wang Yuan-Min, Wang Yong-Sheng, Xu Xu-Rong
Acta Physica Sinica. 2006, 55 (2): 0929 doi: 10.7498/aps.55.929
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The performance of polymer light-emitting diodes was optimized by dispersing titania nanotubes into different functional layers. When titania nanotubes are doped into the hole-transport layer, the hole mobility of the device is greatly increased due to the good p-type conductibility of titania nanotubes. In the case of doping titania nanotubes into emitting layer, irradivative recombination was decreased since organic molecules wrapped on outer surface or entering into the nanotube make the chain conformation of polymer molecules more open. At last, the device efficiency of PLEDs was greatly improved by doping titania nanotubes into the hole buffer layer. This contributes to strong interaction between the titania nanotube and the polymer. This interaction reduces not only the hole conductibility but also the creation of defect states on interface region which can quench the luminescence.

The band structure in microwave frequency for quasi-1-D coaxial photonic crystals

Tong Yuan-Wei, Zhang Ye-Wen, He Li, Li Hong-Qiang, Chen Hong
Acta Physica Sinica. 2006, 55 (2): 0935 doi: 10.7498/aps.55.935
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A quasi-one-dimensional coaxial photonic crystal has been assembled from a series of “tee”,“female” and “male” connectors. With the vector network analyzer the transmission coefficient and the phase information has been measured for different structures. The energy band structure has also been calculated with the method of transmission matrix under Bloch periodicity boundary condition. The experimental results agree well with the calculated results.
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

Growth of carbon nanotips by plasma-enhanced hot filament chemical vapor deposition

Wang Bi-Ben, Xu Xing-Zi, Zhang Bing
Acta Physica Sinica. 2006, 55 (2): 0941 doi: 10.7498/aps.55.941
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Carbon nanotips were prepared by plasma-enhanced hot filament chemical vapor deposition under different bias current using CH4, NH3 and H2 as the reaction gases, and investigated by scanning electron microscopy and micro-Raman spectrometer. The results indicate that the carbon nanotips have graphite structure. With increasing of the bias current, the tip angles of the carbon nanotips are reduced and their growth rate are increased. Combined with theory related to plasma and sputtering, the formation of the carbon nanotips and the change of their growth rate with the bias current are discussed.

Stability of mixed phase silicon thin film material under light soaking

Wang Yan, Han Xiao-Yan, Ren Hui-Zhi, Hou Guo-Fu, Guo Qun-Chao, Zhu Feng, Zhang De-Kun, Sun Jian, Xue Jun-Ming, Zhao Ying, Geng Xin-Hua
Acta Physica Sinica. 2006, 55 (2): 0947 doi: 10.7498/aps.55.947
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Silicon thin films material with different crystalline ratio (Xc) have been deposited with varying silane content of source gases in the PECVD process. We have researched how hydrogen content affects the material and the relationship between micro-structure and optoelectronic properties. Light soaking experiment was then performed. By comparing the changes in the properties before and after irradiation, we conclude that the amorphous region is responsible to the degradation of the photoelectronic property. The mixed phase amorphous silicon degrades less and is more stable than component the common amorphous silicon. The highly crystallized silicon is stable against light soaking. The microcrystalline silicon near the threshold is not so stable as the highly crystallized one, but its optoelectronic property is more suitable than the others for making microcrystalline silicon solar cells.

Effect of lattice site position fluctuation on the electronic structure of DNA

Gao Xu-Tuan, Fu Xue, Song Jun, Liu De-Sheng, Xie Shi-Jie
Acta Physica Sinica. 2006, 55 (2): 0952 doi: 10.7498/aps.55.952
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In the framework of a tight binding model, effect of the lattice site position fluctuation on the energy band and the electronic states of DNA is studied by means of stimulation with the square distribution. Effect of the position fluctuation on the conductivity of DNA is also analyzed. It is found that with the enhancement of the fluctuation the band gap becomes smaller and the electronic states become localized. The electronic states around the bottom of conductance band appear apparently localized with a room temperature fluctuation. Therefore, even if these base pairs were arranged orderly, the band resonant charge transport mechanism might not be suitable for DNA at room temperature.
GENERAL

Approximate analytic solution of land-air couplind dynamical system

Mo Jia-Qi, Wang Hui, Lin Wan-Tao
Acta Physica Sinica. 2006, 55 (2): 0485 doi: 10.7498/aps.55.485
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Atmospheric physics deals with very complicated natural phenomena. Basic models have to be implemented for the sea-air and land-air oscillators and then solve them using the approximate method. In this paper, a class of nonlinear coupling system for land-air oscillator model is studied. Using the homotopic mapping method, it is translated into solving linear problems, and the approximate expressions for the original nonlinear problem are obtained.

Density profile of a superfluid Fermi gas with a phase slip

Wu Hong-Yu, Yin Lan
Acta Physica Sinica. 2006, 55 (2): 0490 doi: 10.7498/aps.55.490
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BEC(Bose Einstein Condensation)-BCS(Bardeen Schrieffer Cooper) crossover is currently one of the main research focuses in the area of cold atoms and BEC. In this paper, we study in detail the phenomenon of a phase slip in a superfluid Fermi gas near a Feshbach resonance, based on our previous work. The density profiles of a superfluid Fermi gas with a phase slip at various temperatures are computed by numerical method. Our results show that the phase-slip phenomenon can provide a direct experimental evidence of the superfluid phase.

Analysis of evolution and life-time of the plasma channel produced by ultra-stort ultra-high power laser pulse

Tang Rong-Rong
Acta Physica Sinica. 2006, 55 (2): 0494 doi: 10.7498/aps.55.494
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Using the perturbed theory, the plasma channel produced by ultra-short ultra-high power laser pulses is considered. Under the actions of recombination, attachment and detachment, the perturbed asymptotic expressions of the density of each kind of charged particles in the course of evolution of the plasma channel are obtained. The influence of each action on the evolution and life_time of the channel is discussed.

Form invariance and non-Noether conserved quantity of generalized Raitzin’s canonical equations of non-conservative system

Qiao Yong-Fen, Zhao Shu-Hong
Acta Physica Sinica. 2006, 55 (2): 0499 doi: 10.7498/aps.55.499
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The form invariance and the non-Noether conserved quantity of generalized Raitzin's canonical equations of non-conservative system are studied. The definition and criterion of the form invariance in the system under infinitesimal transformations are proposed. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally, an example is given to illustrate the application of the result.

Non-Noether conserved quantities for systems with unilateral non-Chetaev nonholonomic constraints

Zhang Yi
Acta Physica Sinica. 2006, 55 (2): 0504 doi: 10.7498/aps.55.504
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This paper studies the symmetries and non-Noether conserved quantities of mechanical systems with unilateral non-Chetaev nonholonomic constraints. The differential equations of motion of the systems are established, and the definitions and criterions of Lie symmetry and Mei symmetry are given. For the unilateral non-Chetaev nonholonomic constraint system, it is proved that under some conditions a new conserved quantity called Hojman conserved quantity can be directly deduced from Lie symmetry, and a new conserved quantity called Mei conserved quantity can be directly deduced from Mei symmetry. The relations between the symmetries and the new conserved quantities are researched. At the end of the paper, an example is given to illustrate the application of the results.

Extended mapping approach and new solutions of the (2+1)-dimensional breaking soliton equations

He Bao-Gang, Xu Chang-Zhi, Zhang Jie-Fang
Acta Physica Sinica. 2006, 55 (2): 0511 doi: 10.7498/aps.55.511
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Extended mapping approach is introduced to solve the (2+1)-dimensional breaking soliton equations. On its basis, abundant propagating and non-propagating structures are found by selecting the arbitrary function appropriately. However, only periodic soliton wave structures are revealed in this paper.

Defect states of homogeneity dislocation structures in two-dimensional phononic crystal

Zhao Fang, Yuan Li-Bo
Acta Physica Sinica. 2006, 55 (2): 0517 doi: 10.7498/aps.55.517
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The defect states in two-dimensional phononic crystal homogeneity dislocation structures has been studied by means of the plane-wave expansion method in combination with a supercell technique. Transverse dislocation structures and longitudinal dislocation structures are investigated respectively. The results show that, acting as a line defect, transverse dislocation structures can mold the flow of sound in the bandgap along the dislocation channel and form the so called waveguides; while longitudinal dislocation structures, which act just as point defects, can form a cavitylike void surrounded by the three nearest cylinders around the dislocation line to create a localized state. In addition, the number and the position of defect bands strongly depend on the transverse and longitudinal dislocation displacement, so we can artificially control the defect bands by adjusting the transverse and longitudinal dislocations of lattices in a homogeneity islocation structures.

Bound states of the Klein-Gordon equation and Dirac equation with the Manning-Rosen scalar and vector potentials

Zhang Min-Cang, Wang Zhen-Bang
Acta Physica Sinica. 2006, 55 (2): 0521 doi: 10.7498/aps.55.521
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The s-wave bound states of the Klein-Gordon equation and Dirac equation with equal Manning-Rosen scalar and vector potentials are obtained, and the solutions are expressed by the hypergeometric function.

Bound states of relativistic particles in the second P?schl-Teller potentials

Zhang Min-Cang, Wang Zhen-Bang
Acta Physica Sinica. 2006, 55 (2): 0525 doi: 10.7498/aps.55.525
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The s-wave bound states of the Klein-Gordon equation and Dirac equation with the Second Pschl-Teller scalar and vector potentials are obtained, and the solutions are expressed in terms of hypergeometric function.

Entanglement decoherence of two-particle entangled states in a noisy environment

Xiang Shao-Hua, Song Ke-Hui
Acta Physica Sinica. 2006, 55 (2): 0529 doi: 10.7498/aps.55.529
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Entanglement decoherence of two particles interacting with the same environment is investigated by means of concurrence and the input-output fidelity. It is found that the entangled states of two-particle system can be divided into two kinds, coherence-preserving states and fragile entangled states. The dynamics of entanglement decoherence for fragile entangled states is discussed by taking into account the ohmic dissipation under the low temperature approximation.

General solution for multi-dimensional coupled and forced quantum oscillator

Xu Xiu-Wei, Ren Ting-Qi, Liu Shu-Yan, Dong Yong-Mian, Zhao Ji-De
Acta Physica Sinica. 2006, 55 (2): 0535 doi: 10.7498/aps.55.535
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Utilizing the general linear quantum transformation theory, we give the exact expressions of evolutionary operator's matrix elements, wave function, expectation value of an observable and partition function, for multi-dimensional coupled and forced quantum oscillator.

The quantum tunneling effect of Reissner-Nordstr?m de Sitter black hole

Li Hui-Ling, Jiang Qing-Quan, Yang Shu-Zheng
Acta Physica Sinica. 2006, 55 (2): 0539 doi: 10.7498/aps.55.539
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Adopting Parikh's mode of quantum radiation as tunneling, the tunneling effect of Reissner_Nordstrm de Sitter black hole is studied. Under implementation of energy conservation, the result shows that the emission of the particle on the event horizon and the cosmic horizon is related with the change of Bekenstein_Hawking entropy and that the spectrum is not precisely thermal.

A kind of Fredholm type weak singular kernel integral equation with triangle function as free term

Wang Li-Min, Ren Chuan-Bo, Xu Shi-Lang, Zhao Xi-Qiang
Acta Physica Sinica. 2006, 55 (2): 0543 doi: 10.7498/aps.55.543
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For a type of Fredholm integral equation with weak singularity integral kernel of logarithm function, the exact solutions is deduced through a calculus procedure when the free term is a triangle function. The singular character of solution is also analyzed when the variable is approaching the extreme points.

Dynamical properties of an asymmetric Josephson junction in Bose-Einstein condensates

Xiao Yu-Fei, Wang Deng-Long, Wang Feng-Jiao, Yan Xiao-Hong
Acta Physica Sinica. 2006, 55 (2): 0547 doi: 10.7498/aps.55.547
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Based on the semiclassical quantum theory, we study the dynamical behaviors of Bose-Einstein condensate in an asymmetric Josephson junction. It is shown that the Josephson effect appears in the system when the ratio χ of the difference of two ground state energies to the interaction energies is zero. When χ≠0, the dynamical behavior of the system shows both the macroscopic quantum tunneling and the macroscopic quantum localization.

Criterion for validity of potential and limiting atom number in a potential well for Bose-Einstein condensation gas

Yu Xue-Cai, Ye Yu-Tang, Cheng Lin
Acta Physica Sinica. 2006, 55 (2): 0551 doi: 10.7498/aps.55.551
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Based on Bose-Einstein condensation at minimized momentum state, a criterion for the validity of potential and the limited atom number loaded in a power law attractive potential well for ultra-cold atom gas is deduced. The criterion gives the required potential intensity when the loaded atom number is defined, or the limited atom number when the potential intensity is decided.

Prediction of chaotic time sequence using least squares support vector domain

Ren Ren, Xu Jin, Zhu Shi-Hua
Acta Physica Sinica. 2006, 55 (2): 0555 doi: 10.7498/aps.55.555
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Starting from the support vector domain model, the paper establishes SVD predictive models of chaos time series as well as chaos phase trace of non-linear map, based on Takens phase space delay reconstructing theory. We adopted the methodof data set as support object elements. Machine self-learning reduces error upper limit of the generalized model. The three chaos time series, Henon/Lorenz/Rossler are predicted by least square. The prediction result indicates that the predictive model makes the set to be mapped into an eigen space of higher dimensions, and the series is predicted by embed dimensions. The predictive error changes with the increase of embed dimension to a constant. Compared with SVM, the SVD requires smaller support vector, and has faster convergence rate. It has robustness characteristics with adaptive flexible kernel function choice. The predicted net points are ten to twenty times more than SVM. Under the conditions of small sample, non-linear, and unknown probability density, the predicted series is in concordance with the series′ true value.

Recovery of statistical property of initial conditions based on time-varying parameter from coupled map lattices

Liu Ying, Shen Min-Fen, Chan Francis H. Y.
Acta Physica Sinica. 2006, 55 (2): 0564 doi: 10.7498/aps.55.564
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To recover the initial conditions of coupled map lattices (CML), which goes athwart the coupled systems, is one of key tasks of signal processing. Based on thecommon symbolic dynamic method, a novel time-varying symbolic dynamic method is proposed. The Logistic map is used to test the properties of the method. Numerical simulation shows that the new scheme can recover the statistical property of the initial conditions from coupled map lattices for both noiseless and noisy signals. The performance of the proposed method is significantly superior to the common method. Moreover, the proposed algorithm has small biases, small mean square errors and a high correlation for the given data. Our new approach is more appropriate to the analysis of practical systems and measurement of coupled systems.

Calculation of the maximal Lyapunov exponent from multivariate data

Lu Shan, Wang Hai-Yan
Acta Physica Sinica. 2006, 55 (2): 0572 doi: 10.7498/aps.55.572
Full Text: [PDF 159 KB] Download:(2079)
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According to the method of calculating maximal Lyapunov exponent (MLE) from univariate small data sets, an extended method based on multivariate time series is proposed. The extended method can search out optimal reconstructing parameters to meet the requirement of the original method for reconstructing multivariate phase space, and the method can compute the MLE by making use of the optimal reconstructed multivariate phase space. The method is tested by coupled non-identical chaotic Rssler, coupled chaotic Rssler and hyper chaotic Rssler. The test results show that the extend method is efficient, and the computing results of MLE based on multivariate are much closer to the theoretical values than the results of univariate even when the data sets of each time series become small.

Parameter estimation for chaotic system based on particle swarm optimization

Gao Fei, Tong Heng-Qing
Acta Physica Sinica. 2006, 55 (2): 0577 doi: 10.7498/aps.55.577
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It's of vital importance to estimate the unknown parameters of chaos systems in chaos control and synchronization. We firstly improve the newly developed particle swarm optimization (PSO) in view of the population initialization and objective function treatment. Then we use the improved algorithms for parameter estimation and on-line estimation of chaotic system for its global searching ability. Experiments show that the improved method has better adaptability, reliability and high precision is robust to noise. It is proved to be a successful approach in parameter estimation for chaotic systems.

Energy band structure of two ions in a one-dimensional Paul trap

Wu Yun-Wen, Hai Wen-Hua, Cai Li-Hua
Acta Physica Sinica. 2006, 55 (2): 0583 doi: 10.7498/aps.55.583
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Making use of the well-known truncated-series method, we give a numerical program to calculate the exact solutions of two Coulomb-correlated ions confined in a linear Paul trap. The discrete motion state functions and energy spectra are obtained for the trap frequencies approaching the experimentally realizable limiting values, which correspond to a denumerable infinite point-set of the frequencies. Continuously varying the trap frequency between two neighboring points of the denumerable infinite set, from the quantum perturbation technique we find the energy-band structure based on the exact discrete spectra in which the bands are narrower and the gaps wider. The band structure can influence the laser cooling of Paul trapped ions and the quantum logic operation based on the system that should be considered in the corresponding experiments thereby.

Generalized synchronization of two non-identical systems

Li Fang, Hu Ai-Hua, Xu Zhen-Yuan
Acta Physica Sinica. 2006, 55 (2): 0590 doi: 10.7498/aps.55.590
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Generalized synchronization of two non-identical systems is studied based on Temam's inertia manifold theory of infinite dimensional dynamical systems. On the assumption that both systems have absorbing sets and attractors, the generalized synchronization manifold, which has the property of Lipschitz smoothness, invariance and exponential absorption, can be attained by defining a fixed point in a class of functions. Simulation results validate the theory.

Linear state feedback control for a new chaotic system

Li Rui-Hong, Xu Wei, Li Shuang
Acta Physica Sinica. 2006, 55 (2): 0598 doi: 10.7498/aps.55.598
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The problem of controlling a class of new chaotic system is investigated. Applying Routh-Hurwitz criterion, we analyze the stability of the controlled system. The choice principle of feedback coefficients to attain control objective is proved strictly by combining the linear state feedback method. Numerical simulation results show that the method can effectively guide the chaotic trajectories to an unstable equilibrium point or periodic solution. In addition, we find the control is stable in the presence of weak external noise.

Parameter identification and adaptive synchronization of uncertain Chen system

Wang Xing-Yuan, Wu Xiang-Jun
Acta Physica Sinica. 2006, 55 (2): 0605 doi: 10.7498/aps.55.605
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This paper addresses the adaptive synchronization and parameter identification problem of two Chen systems with unknown system parameters. Based on the Lyapunov stability theory, an adaptive controller and the parameter update rule are designed. It is proved that the controller and update rule can make the states of the drive system and the response system with unknown parameters asymptotically synchronized, and identify the system parameters. Numerical simulations show the effectiveness of the adaptive controller.

Period-doubling bifurcation of a double-well Duffing-van der Pol system with bounded random parameters

Sun Xiao-Juan, Xu Wei, Ma Shao-Juan
Acta Physica Sinica. 2006, 55 (2): 0610 doi: 10.7498/aps.55.610
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Period-doubling bifurcation in a double-well Duffing-van der Pol system with bounded random parameters and subject to harmonic excitations is studied. The random system is reduced to its equivalent deterministic one by the Chebyshev polynomial approximation, through which the response of the random system can be obtained by deterministic numerical methods. Numerical simulations show that similar to their counterparts in deterministic nonlinear systems, period-doubling bifurcation may occur in the random Duffing-van der Pol system, and that the period-doubling bifurcation of the random_parameter system has its own characteristics. Numerical results also show that the Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear systems with random parameters.

Bifurcation control for a non-autonomous system with two time delays

Qian Chang-Zhao, Tang Jia-Shi
Acta Physica Sinica. 2006, 55 (2): 0617 doi: 10.7498/aps.55.617
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A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.

Bifurcation analysis and control in Turbo decoding algorithm

Zhang Wei, Zhou Shu-Hua, Ren Yong, Shan Xiu-Ming
Acta Physica Sinica. 2006, 55 (2): 0622 doi: 10.7498/aps.55.622
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Turbo Codes can approach the Shannon limit very closely with the help of its special iterative decoding algorithm. This paper establishes a nonlinear dynamic system to analyze the relationship between Turbo decoding output and the number of iterations. Here, the number of iterations is taken as the time axis, decoding output as the state variable, SNR and information bits N as system parameters. It is shown that with SNR increasing, the decoding algorithm undergoes three stages, namely the indecisive fix-point, singular region and unequivocal fix-point. Bifurcations occur during the transformation from the indecisive fix-point to the singular region. It is first proposed that fold, period doubling and Neimark-Sacker bifurcation all have the possibility to occur, depending on the value of N. In the singular region, phase trajectories may appear as period-two, period-three, quasiperiod and chaos. This paper first observed and confirmed the existence of period-three and chaos. Singular region deteriorates the performance of Turbo codes under low SNR. This paper proposes a time-delay feedback control method to stablize the fix-point. Simulation results show that this method achieves 0.1—0.3 dB improvement for Turbo codes under low SNR condition.

A nonlinear wave equation and exact periodic solutions in circular-rod waveguide

Liu Zhi-Fang, Zhang Shan-Yuan
Acta Physica Sinica. 2006, 55 (2): 0628 doi: 10.7498/aps.55.628
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Under the condition of small deformation, a new nonlinear wave equation is derived to describe nonlinear wave evolution in a nonlinear elastic circular rod by means of Hamilton principle. The nonlinear constitutive relationship proposed by Cox and transverse Possion effects are simultaneously taken into account. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic cosine function expansion method. The exact periodic solutions of these nonlinear equations are obtained. The limiting conditions of these solutions are also given.

Multiple velocity difference model and its stability analysis

Wang Tao, Gao Zi-You, Zhao Xiao-Mei
Acta Physica Sinica. 2006, 55 (2): 0634 doi: 10.7498/aps.55.634
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Based on the full velocity difference (FVD) model proposed by Jiang and Wu, we present an extended car_following model, called the multiple velocity difference (MVD) model. We attempt to enhance the stability of the traffic flow by using the velocity differences of multiple vehicles. It can be found that the critical value of the sensitivity in the MVD model decreases and the stable region is apparently enlarged, compared with the FVD model. Additionally, the simulated results suggest that the MVD model can suppress the traffic jam effectively.

Analog implementation of wavelet transform based on switched-current filter circuits

Hu Qin-Chun, He Yi-Gang, Guo Di-Xin, Li Hong-Min
Acta Physica Sinica. 2006, 55 (2): 0641 doi: 10.7498/aps.55.641
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A general scheme for the analog implementations of wavelet transform using switched_current (SI) filter circuits is presented. SI circuits are well suited for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by both the transconductance ratios (W/L) and the clock frequency. The circuits are composed of analog filter banks whose impulse responses are the first derivative of Gaussian and its dilations. The transfer functions of the basic wavelet filter can be given by Pad approximation, which can decompose the transfer function into rational form so as to be conveniently implemented by SI circuits. Therefore, it can easily be applied to other filters with a prescribed impulse response. Simulated results indicated a good performance of wavelet transform.

Effects of high magnetic fields on the distribution of Si in solidified structures of Al-Si alloy

Wang Chun-Jiang, Wang Qiang, Wang Ya-Qin, Huang Jian, He Ji-Cheng
Acta Physica Sinica. 2006, 55 (2): 0648 doi: 10.7498/aps.55.648
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In order to find the effects of high magnetic fields on the solidification processes of metallic materials, the changes of solidified structures of Al-14.98% Si and Al-9.2% Si alloys were examined in this study. The alloys were solidified under different magnetic field conditions, and then the distribution and morphologies of Si element in the solidified structures was analyzed. It is found that uniform magnetic fields and gradient magnetic fields can affect the solidified structures of the alloy by Lorenz force and magnetization force respectively, and the imposed magnetic fields also can change the distribution of primary Si crystals in the alloy remarkably. The primary Si crystals distributed homogeneously under uniform magnetic field conditions, while they congregated at the upside or downside of samples by the combined action of buoyancy and magnetization force under gradient magnetic field conditions. Furthermore, the morphologies of eutectic crystals in the alloy were changed by the magnetic fields and the layer thickness of eutectic crystals were different at the upside and downside under gradient magnetic field. Both theoretical analysis and examinations indicated that magnetic energy also affected the solidifying process, the content of eutectic aluminum in eutectic structure increased and eutectic point left-shifted when Al-Si alloy solidified under high magnetic fields.
ATOMIC AND MOLECULAR PHYSICS

Effects of relaxation induced by excitation (or ionization) of inner subshell electrons on the wave functions and transition probabilities

Li Jie, Dong Chen-Zhong, Xie Lu-You
Acta Physica Sinica. 2006, 55 (2): 0655 doi: 10.7498/aps.55.655
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The relaxation effects induced by excitation (or ionization) of inner subshell electrons and their influences on the electronic wave functions of the ground configuration 3p6 and five excited configurations 1s-14s, 2s-14s, 2p-14s, 3s-14s, and 3p-14s in Argon have been systematically studied by using the Multi_configuration Dirac_Fock method (MCDF). Furthermore, the transition energies and probabilities of argon from kα and kβ lines have been presented and discussed in cases with and without relaxation, and also a comparison has been made with some existing theoretical calculations.

Cluster-assisted multiple ionization of acetone by intense nanosecond laser

Xiao Xue, Li Hai-Yang, Luo Xiao-Lin, Niu Dong-Mei, Wen Li-Hua, Wang Bin, Liang Feng, Hou Ke-Yong, Dong Can, Shao Shi-Yong
Acta Physica Sinica. 2006, 55 (2): 0661 doi: 10.7498/aps.55.661
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The photoionization of acetone seeded in helium is studied by time_of_flight mass spectrometry using a 25 ns, 532 nm Nd: YAG laser with intensity in the range of 1010—1011 W/cm2. Multiply charged ions of Op+(p=2—4) and Cq+(q=2—4) of tens of eV have been observed when the laser beam irradiates the most dense part of the pulsed molecular beam. The intensity and the kinetic energy of the multiply charged ions increase with the increasing of the laser energy. An electron re_scattering and re_colliding ionization model is proposed to explain the appearance of the multiply charged ions under such low laser intensity.

Simulation of sodium atom deposition pattern in a laser standing wave field

Ma Bin, Ma Yan, Zhao Min, Ma Shan-Shan, Wang Zhan-Shan
Acta Physica Sinica. 2006, 55 (2): 0667 doi: 10.7498/aps.55.667
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A grating structure with the period of half of the laser wavelength is formed by focusing the atoms with a nearly resonant laser standing wave field. The motion of sodium atoms traversing an unsaturated potential are studied by the semi_classical approximation. The structures of gratings under various conditions were simulated using numerical method. By characterizing the grating with FWHM and contrast, the influence of some factors, such as the transverse temperature, the longitudinal velocity, and the free flight to the atom deposition are analysed. Our work provides a theoretical basis to the ongoing atom lithography experiment.

Electron emission induced by the interaction of highly charged ions 207Pbq+(24≤q≤36) with solid surface of Si(110)

Wang Yu-Yu, Zhao Yong-Tao, Xiao Guo-Qing, Fang Yan, Zhang Xiao-An, Wang Tie-Shan, Wang Shi-Wei, Peng Hai-Bo
Acta Physica Sinica. 2006, 55 (2): 0673 doi: 10.7498/aps.55.673
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The electron emission induced by highly charged ions 207Pbq+(24≤q≤36) interacting with Si(110) surface is reported. The result shows that the electron emission yield Y has a strong dependence on the projectile charge state q, incidence angle ψ and impact energy E. In fitting the experimental data we found a nearly 1/tanψ dependence of Y. Theoretical analysis shows that these processes are closely related to the process of potential electron emission based on the classical over_the_barrier model.
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

Wavelet-based multifractal analysis of ground electric field before occurrence of strong discharge in thunderstorm

Gou Xue-Qiang, Zhang Yi-Jun, Dong Wan-Sheng
Acta Physica Sinica. 2006, 55 (2): 0957 doi: 10.7498/aps.55.957
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It is considered that complex systems far from equilibrium are evolved in avalanche and self similar multiplicative cascade way, and have characteristics of multifractality. By using the ground electric field data obtained in the middle of Qinghai-Xizang plateau region, multifractal behavior of lightning discharges in thunderstorm is investigated with wavelet-based multifractal method. It is found that strong singularity and multfractality are involved in the strong lightning discharges, the minimum exponent αmin is less than -0.3, and the width of spectrum Δα is greater than 1.6, and the scaling behavior is consistent with the modified version of the binomial multiplicative cascade multifractal model. It is also shown that Δα increases with the enhancing of the discharge activity, and strong lightning happens in regions where Δα is high or is decreasing, the related reason is discussed.

A technique for distinguishing dynamical species in the temperature time series of Yangtze River delta

Feng Guo-Lin, Hou Wei, Dong Wen-Jie
Acta Physica Sinica. 2006, 55 (2): 0962 doi: 10.7498/aps.55.962
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The conditional entropy of two symbolic sequences which are encoded faithfully from two different time series is minimized at the zero relative shift of the two time series if the two time series have their origins in the same underlying dynamics. This technique is also useful in studying the delayed coupling between different time series. Applications are made to the temperature data derived from five meteorological stations in China, namely Shanghai, Nantong, Changzhou, Nanjing and Hangzhou in order to test the commonality of their underlying dynamics, obtain the relative strength of the dynamics coupling between different variables, and extract the implicit delayed information in the dynamics.

On the predictability of the Lorenz system

He Wen-Ping, Feng Guo-Lin, Dong Wen-Jie, Li Jian-Ping
Acta Physica Sinica. 2006, 55 (2): 0969 doi: 10.7498/aps.55.969
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Regarding Lorenz model as the forecast equation,this paper investigates the evolution of the number of particles falling into the predefined dynamic window and the average forecast weight X of the Lorenz system. Then we research preliminarily the predictability of the Lorenz system from another point of views, and the influence of the Gaussian white noises on the Lorenz system. The results show that the evolution of the number reflects the predictability of the Lorenz system to a certain extent. For initial value sets in different areas, there are different predictabilities of the Lorenz system, and we find that there are different influences on the Lorenz system from the Gaussian white noises.

Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere

Ji Xiao-Ling, Huang Tai-Xing, Lü Bai-Da
Acta Physica Sinica. 2006, 55 (2): 0978 doi: 10.7498/aps.55.978
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Based on the extended Huygens-Fresnel principle, the spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere is studied by using the incoherent superposition of higher-order Hermite-Gaussian beams. The analytic expression of the mean-squared width of partially coherent cosh-Gaussian beams in turbulence is derived. It is shown that the spreading increases with increasing turbulent parameter C2n and decentered parameter δ of the beams. However, partially coherent cosh-Gaussian beams with larger δ are less sensitive to the effect of turbulence than those with smaller δ.

Raman lidar for profiling atmospheric CO2

Hong Guang-Lie, Zhang Yin-Chao, Zhao Yue-Feng, Shao Shi-Sheng, Tan Kun, Hu Huan-Ling
Acta Physica Sinica. 2006, 55 (2): 0983 doi: 10.7498/aps.55.983
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Based on laser atmosphere backscattering spectrum, the design and experiment of a Raman lidar system for measurement of atmospheric CO2 are presented. 354.7nm third harmonic of Nd∶YAG laser is transmitted with 350mJ pulse energy and repetition rate of 20Hz. The receiver employs a photomultiplier tube with quantum efficiency of 25% and 200MHz photon counter, and it detects Raman backscattering 371.66nm(shift 1285cm-1) signal. At 1h integration, the signal to noise ratio below 2.5km is greater than 8. Combinatorial filter is used to reject interference presented by 354.7nm intense Mie-Rayleigh backscattering and 375.4nm Raman backscattering from O2. We compare the Raman return signal at 371.66nm from atmospheric CO2 with the reference Raman return signal at 386.7nm from atmospheric N2 to retrieve the atmospheric CO2 concentration.

Analysis of the correlation between γ-ray and radio emissions from γ-ray loud Blazar using the discrete correlation function

Cheng Yong, Zhang Xiong, Wu Lin, Mao Wei-Ming, You Li-Sha
Acta Physica Sinica. 2006, 55 (2): 0988 doi: 10.7498/aps.55.988
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In this paper, we collect 119 γ-ray-loud Blazar (97 flat spectrum radio quasars (FSRQs) and 22 BL Lacertae objects (BL Lac)),and investigate respectively the correlation between the γ-ray emission (maximum, minimum, and average data) at 1GeV and the radio emission at 8.4GHz by discrete correlation function (DCF) method. Our main results are as follows: there is good correlation between the γ-ray in high state and average state and radio emissions for the whole 119 Blazar and 97 FSRQs. And there are no correlation between γ-ray emission and radio emission in low state. Our result shows that the γ-rays are associated with the radio emission from the jet, and that the γ-ray emission is likely to have come from the synchrotron self-Compton model (SSC) process in this case.

Quantum entropy of cylindrical black hole in Anti-de Sitter space-time

Li Gu-Qiang
Acta Physica Sinica. 2006, 55 (2): 0995 doi: 10.7498/aps.55.995
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By using the brick-wall model, the quantum entropy of a cylindrical black hole in Anti-de Sitter space-time arising from the massless Dirac field is discussed. It is shown that the quantum entropy has both linear and logarithmical divergences if the usual contribution from the vacuum surrounding the system is ignored, and the whole expression does not take the form of the scalar one. Both the whole logarithmic term and the subleading logarithmic term which relates to the spins of the Dirac particles are always positive.
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