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Chin. Phys. B  
  Chin. Phys. B--2002, Vol.11, No.8
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Bound states of the Klein-Gordon and Dirac equations for scalar and vector harmonic oscillator potentials

Qiang Wen-Chao
Chin. Phys. B 2002, 11 (8): 0757;  doi: 10.1088/1009-1963/11/8/001
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We give the exact bound states of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials.

Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems

Li Ren-Jie, Qiao Yong-Fen, Liu Yang
Chin. Phys. B 2002, 11 (8): 0760;  doi: 10.1088/1009-1963/11/8/002
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We present a general approach to the construction of conservation laws for variable mass nonholonomic nonconservative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditions for the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally, we give an example to illustrate the application of the results.

Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints

Zhang Hong-Bin, Gu Shu-Long
Chin. Phys. B 2002, 11 (8): 0765;  doi: 10.1088/1009-1963/11/8/003
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In this paper we study the Lie symmetries of Birkhoff systems with unilateral constraints. We give the conditions for, and the form of, conserved quantities due to the Lie symmetries of the systems, and we also study the inverse problem of the Lie symmetries of the systems. Finally, an example is given to illustrate the application of the results.

A mean-field approximation scheme containing the spatial parameter and its application to a surface-reaction-like cellular automaton model

Yu Zhong-Qiu, Zhang Zhen, Zhang Bo-Tao
Chin. Phys. B 2002, 11 (8): 0771;  doi: 10.1088/1009-1963/11/8/004
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Using an AB2 surface-reaction-like cellular automaton model, we present a modified mean-field approximation scheme for describing some dynamic lattice models, in which a lattice freedom parameter N is introduced as a variable. We obtain the phase diagrams of the example model for linear, hexagonal, square and triangular lattices, and we reveal a second-order phase transition which has not been found using traditional approaches.

Lipid membrane: inelastic deformation of surface structure by an atomic force microscope

Zhang Jing, Sun Run-Guang
Chin. Phys. B 2002, 11 (8): 0776;  doi: 10.1088/1009-1963/11/8/005
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The stability of the 1,2-Dioleoyl-sn-Glycero-3-[phospho-rac-1-Glycerol-Na] liposome in the liquid crystalline state have been investigated using an atomic force microscope (AFM). We have observed the inelastic deformation of the sample surface. The AFM tip causes persistent deformation of the surface of the lipid membrane, in which some of the lipid molecules are eventually pushed or dragged by the AFM tip. The experiment shows how the surface structure of the lipid membrane can be created by the interaction between the AFM tip and lipid membrane. When the operating force exceeds 10-8 N, it leads to large deformations of the surface. A square region of about 1×1μm2 is created by the scanning probe on the surface. When the operating force is between 10-11N and 10-8N, it can image the topography of the surface of the lipid membrane. The stability of the sample is related to the concentration of the medium in which the sample is prepared.

The relationship between four-dimensional θ=π Yang-Mills theory and the two-dimensional Wess-Zumino-Novikov-Witten model

Kou Su-Peng
Chin. Phys. B 2002, 11 (8): 0785;  doi: 10.1088/1009-1963/11/8/006
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Used the dimensional reduction in the sense of Parisi and Sourlas, the gauge fixing term of the four-dimensional Yang-Mills field without the theta term is reduced to a two-dimensional principal chiral model. By adding the θ term (θ=π), the two-dimensional principal chiral model changes into the two-dimensional level 1 Wess-Zumino-Novikov-Witten model. The non-trivial fixed point indicates that Yang-Mills theory at θ=π is a critical theory without mass gap and confinement.

Influence of the randomly varying domain length of quasi-phase-matched crystals on quadrature squeezing performance

Li Yong-Min, Wu Ying-Rui, Zhang Kuan-Shou, Xie Chang-De, Peng Kun-Chi
Chin. Phys. B 2002, 11 (8): 0790;  doi: 10.1088/1009-1963/11/8/007
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During the fabrication of quasi-phase-matched (QPM) devices, errors of periodic structure are usually inevitable. The errors result in the deviation of the actual periodic domain length from the theoretical value. In this paper, we numerically analyse the influence of errors on the quadrature squeezing performance of a degenerate optical parametric amplifier consisting of QPM devices. It is shown that errors significantly degrade the squeezing degree of the quadrature squeezed light. Due to the presence of the errors, the relative phase between the signal and the pump field for obtaining the maximum squeezing depends on the propagation distance of light in the crystal and the pump power.

L-shell absorption measurement and simulation of x-ray-heated constrained material

Liu Hong-Jie, Zhang Bao-Han, Yang Guo-Hong, Li Jun, Zhang Ji-Yan, Yang Jia-Min, Yan Jun, Li Jia-Ming
Chin. Phys. B 2002, 11 (8): 0795;  doi: 10.1088/1009-1963/11/8/008
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Using the newly-designed multi-layered target, we obtain a homogeneous Al sample plasma at high density, low electron temperature, and in near local thermodynamic equilibrium. L-shell resonance absorption lines of Li-like and Be-like ions, as well as satellites are clearly observed. Transition arrays such as 2s-3p, 2s2-2s3p and 2s2p-2p3p are identified. We present the calculation method based on the unresolved transition array model, and we compare the measured transmission spectrum with the calculated results. The electron temperature of the constrained sample plasma is determined to be 34eV with a variation of ±2eV.

Analysis of dusty plasma in the positive column of glow discharges

Wang De-Zhen, Wu Hong-Tao
Chin. Phys. B 2002, 11 (8): 0799;  doi: 10.1088/1009-1963/11/8/009
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The radial distributions of ions, electrons and dust particles in the positive column of glow discharges are investigated in a triple-pole diffusion model. The dust particles are mainly trapped in the region around the column axis where the electrostatic potential is the highest. The presence of the dust particles results in the ion density increasing and the electron density decreasing in the dust-trapped region. The dust-trapped region is wider for a higher dust temperature or a smaller particulate radius. The ions and electrons in the dust-free region away from the column axis are in ambipolar diffusion.

Field-ion microscopy observation of single-walled carbon nanotubes

Zhang Zhao-Xiang, Zhang Geng-Min, Du Min, Jin Xin-Xi, Hou Shi-Min, Sun Jian-Ping, Gu Zhen-Nan, Zhao Xing-Yu, Liu Wei-Min, Wu Jin-Lei, Xue Zeng-Quan
Chin. Phys. B 2002, 11 (8): 0804;  doi: 10.1088/1009-1963/11/8/010
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Field-ion microscopy (FIM), a tool for surface analysis with atomic resolution, has been employed to observe the end structure of single-walled carbon nanotubes (SWCNTs). FIM images revealed the existence of open SWCNT ends. Amorphous carbon atoms were also observed to occur around SWCNTs and traditional field evaporation failed to remove them. Heat treatment was found to be efficacious in altering the end structures of SWCNT bundles. Carbon and oxygen atoms released from heated tungsten filament are believed to be responsible for the decoration imposed on the SWCNT ends.

The soliton properties of dipole domains in superlattices

Zhang Qi-Yi, Tian Qiang
Chin. Phys. B 2002, 11 (8): 0809;  doi: 10.1088/1009-1963/11/8/011
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The formation and propagation of dipole domains in superlattices are studied both by the modified discrete drift model and by the nonlinear Schr?dinger equation. The spatiotemporal distribution of the electric field and electron density are presented. The numerical results are compared with the soliton solutions of the nonlinear Schr?dinger equation and analysed. It is shown that the numerical solutions agree with the soliton solutions of the nonlinear Schr?dinger equation. The dipole electric-field domains in semiconductor superlattices have the properties of solitons.

Electronic structure of hexagonal quantum-disc clusters

Wang Li-Min, Luo Ying, Ma Ben-Kun, Liu Cheng-Shi
Chin. Phys. B 2002, 11 (8): 0812;  doi: 10.1088/1009-1963/11/8/012
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Within the effective-mass approximation, we investigate the electronic structure of hexagonal quantum-disc clusters using the finite element method. With an increasing amount of quantum dots in the cluster, the electronic energy levels quickly expand into mini-bands, each consisting of discrete, unevenly distributed energy levels. The corresponding electronic eigenfunctions are linear combinations of the electron orbits in each quantum dot. The spatial symmetry of the combination is the same as the electronic eigenfunction of a single quantum dot.

The flavour liquid state and Hund's rule effects in spin systems with orbital degeneracy

Shi Da-Ning, Yang Zhi-Hong
Chin. Phys. B 2002, 11 (8): 0817;  doi: 10.1088/1009-1963/11/8/013
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In order to understand the properties of the spin system with orbital degeneracy, we first generalize the linearized semiclassical spin wave method for the SU(2) generators into the SU(4) case, and then investigate the elementary excitations of the orbital-spin systems in the SU(4) limit. The results show that, due to the reduction of the dimensionality of the excitations, the ordered state of the SU(4) spin-orbital model is unstable. Secondly, we study the effects of the Hund interaction on the flavour liquid state of the system. Our mean-field results suggest that, for a small Hund interaction, the flavour liquid state is still stable against the generalized spin-density wave state, but with sufficient deviation from the SU(4) limit, the long-range order may be attained in two-dimensional systems. Finally, the implications for the experimental observations on the material LiNiO2 are discussed.

Properties of the ground state in a spin-2 transverse Ising model with the presence of a crystal field

Jiang Wei, Wei Guo-Zhu, Du An, Zhang Qi
Chin. Phys. B 2002, 11 (8): 0823;  doi: 10.1088/1009-1963/11/8/014
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The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal field are studied by using the effective-field theory with correlations. The longitudinal and transverse magnetizations, the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice (z=3).

Zero-field-cooled and field-cooled magnetizations and magnetic susceptibility of itinerant ferromagnet SrRuO3

Hou Deng-Lu, Jiang En-Yong, Bai Hai-Li
Chin. Phys. B 2002, 11 (8): 0827;  doi: 10.1088/1009-1963/11/8/015
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Zero-field-cooled (ZFC) magnetization, field-cooled (FC) magnetization, ac magnetic susceptibility and major hysteresis loops of itinerant ferromagnet SrRuO3 have been measured at magnetic ordering temperatures ranging from 5 to 160 K. An empirical model is proposed to calculate the measured ZFC magnetization. The result indicates that the calculated ZFC magnetization compares well with the measured one. Based on the generalized Preisach model, both the ZFC and FC curves are reproduced by numerical simulations. The critical temperature and critical exponents are determined by measuring the ac magnetic susceptibility in different bias magnetic fields at temperatures in the vicinity of the point of phase transition.

A two-dimensional photonic crystal with six large bandgaps formed by a hexagonal lattice of anisotropic cylinders

Zhuang Fei, Wu Liang, He Sai-Ling
Chin. Phys. B 2002, 11 (8): 0834;  doi: 10.1088/1009-1963/11/8/016
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The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a hexagonal structure of anisotropic cylinders. Two cylindrical inclusions in the unit cell have two different radii, R1 and R2 (R12). By reducing the symmetry of the structure and choosing appropriately parameters R2 and s=R1/R2 (s<1), we obtain six large complete bandgaps, among which three are over 0.05 ωe (where ωe=\frac{2πc}{a}) in the high region of the normalized frequency (however, one of these over 0.065 ωe is not stable). There are two other stable complete bandgaps in the low-frequency region.
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