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Superconvergence for L^2-projection in finite elements

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Chinese Science Bulletin 1998年第1期43卷 22-24页

作者： CHEN Chuanmiao institute of Computing, hunan normal university, changsha 410081, china hunan normal university Institute of Computing Changsha China

Two classes of superconvergence points for L 2 projection u\-n in n degree finite elements on uniform grids are shown by element analysis method. Superconvergence points of u n are n+1 order Gauss point G n+1 for odd d≥1 (so the endpoint of each element is of superconvergent), and n+1 order pointset Z n+1 for even n ≥2 (which includes the endpoints and midpoint), respectively. Symmetry point is only an important part of them.

关键词： superconvergence finite elements L 2 projection.

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

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Communications in Theoretical physics 2007年第7期48卷 125-131页

作者： FANG Jian-Shu LIU Wing-Ki ZHU Shan-Hua1 institute of physics,hunan university of Technology,Zhuzhou 412008,china2 department of physics,hunan normal university,changsha 410081,china3 department of physics,university of Waterloo,Waterloo,Ontario,Canada N2L 3G1 institute of physics Hunan University of Technology Zhuzhou 412008 China

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional pe-riodic optical lattice *** stationary state perturbation solutions of the coupled two-component nonlinearSchr?dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation *** analysisrevels that the perturbation solution is the chaotic one,which indicates the existence of chaos and chaotic region inparameter *** corresponding numerical calculation results agree well with the analytical *** applying thechaotic perturbation solution,we demonstrate the atomic spatial population and the energy distribution of the systemare chaotic generally.

关键词： stationary state classical chaos two-component Bose-Einstein condensates optical lattice potential

SYMMETRIC POINT STRUCTURE OF SUPERCONVERGENCE FOR CUBIC TRIANGULAR ELEMENTS -A CONSULTATION WITH ZHU

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Journal of Computational Mathematics 2003年第6期21卷 727-732页

作者： Chuan-miao Chen (institute of Computation, hunan normal university, changsha 410081, china) institute of Computation Hunan Normal University Changsha 410081 China

Superconvergence structures for rectangular and triangular finite elements are summarized. Two debatable issues in Zhu's paper [18] are discussed. A superclose polynomial to cubic triangular finite element is construc... 详细信息

关键词： Cubic triangular element Superconvergence Symmetric points.

Hopping Wave Function in Quantum Kicked Systems

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原子与分子物理学报 2003年第1期20卷 107-113页

作者： CHONG Gui-shu,HAI Wen-huaCorrespondence Author (1.department of physics, hunan normal university, changsha, 410081, china) department of physics Hunan Normal University Changsha 410081

A model of a kicked particle in an infinite potential well is studied. We presented the wave functions of the system applying a direct perturbation method. Theoretical analyses and numerical calculations show that the wave function is discontinuous across each kicking instant. As an extension of this result, we find that the wave function of any periodically kicked system usually has this property. Therefore, at each kicking instant, the wave function chooses randomly between the limits on either side and may be hopping.

关键词：原子物理学结构波函数量子体系

Analytical study of stationary soliton excitations in diamond-structure chain with quartic anharmonicity

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原子与分子物理学报 2001年第2期18卷 143-149页

作者： XIA Qing lin 1, ZHOU Guang hui 2, YAN Jia ren 2 (1.department of Applied physics and Heat Engineering, Central South university, hunan changsha 410083 2.department of physics, hunan normal university, hunan changsha 410081) 中南大学湖南长沙 410083 湖南师范大学湖南长沙 410081

This work analytically study soliton excitations in an one dimensional chain with the same mass but two alternating force constants between the nearest neighbors by means of multiple scales method plus quasi discrete approximation. This model simulates a row of atoms in the 〈111〉 direction of a diamond structure type of crystals. The explicit expressions of the stationary soliton solutions are obtained at some special wave vectors of the carrier wave ( q =±π/ a for acoustic mode and q=0 , ±π/ a for optical mode). The configuration of the atomic displacements of this model is different from that of diatomic chain with quartic anharmonicity.

关键词： Stationary soliton excitation Diamond structure Multiple scales method Quasi discrete approximation

D-Dimensional Dirac Fermions BEC-BCS Crossover Thermodynamics

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Communications in Theoretical physics 2007年第7期48卷 99-106页

作者： CHEN Ji-Sheng institute of Particle physics & physics department,Central china normal university,Wuhan 430079,china institute of Particle physics Central China Normal University physics department Central China Normal University

An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentzvector condensation effects on the equation of state of the strongly interacting fermions *** interior quantumfluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized ThomsonProblem counterterm *** general analytical formulas for the d-dimensional thermodynamics are given nearthe unitary limit region,In the non-relativistic limit for d=3,the universal dimensionless coefficientε=4/9 andenergy gap △/ε_f=5/18 are reasonably consistent with the existing theoretical and experimental *** the unitarylimit for d=2 and T=0,the universal coefficient can even approach the extreme occasion ξ=0 corresponding to theinfinite effective fermion mass m~*=∞,which can be mapped to the strongly coupled two-dimensional electrons and isquite similar to the three-dimensional Bose-Einstein condensation of ideal boson ***,for d=1,the universalcoefficient ξ is negative,implying the non-existence of phase transition from superfluidity to normal *** solutionsmanifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.

关键词： unitary fermions thermodynamics BEC-BCS crossover statistical methods

Scattering and absorption of particles by a black hole involving a global monopole

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Chinese physics B 2012年第4期21卷 134-137页

作者：邵建舟王永久 institute of physics Hunan Normal UniversityChangsha 410081China

Under the conditions that the wavelength of a particle is much larger than its radius of central mass, and the Schwarzschild field is weak, the scattering of a particle has been studied by many researchers. They obtained that scalar and vector particles abide by Rutherford＇s angle distribution by using the low level perturbation method and the scattered field＇s approximation in a weak field. The scattering cross section of a photon coincides with the section in Newton＇s field of point mass. We can obtain the photon＇s polarization effect by calculating the second-order perturbation in the linear Schwarzschild field. This article discusses the scattering and absorption of a particle by a black hole involving a global monopole by using the aforesaid method.

关键词： scattering absorption black hole wave function

A New Type of High Frequency Vibrational Modes for Diatomic Chain with Quartic Substrate Nonlinearity

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原子与分子物理学报 1998年第3期 141-145页

作者： department of physics and institute for Nonlinear science, hunan normal university, changsha hunan 410081Hu Xiangyuedepartment of physics, changsha Railway university, changsha hunan 410075 Li LequnShaoyang College of education,Shaoyang

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ＡＮｅｗＴｙｐｅｏｆＨｉｇｈＦｒｅｑｕｅｎｃｙＶｉｂｒａｔｉｏｎａｌＭｏｄｅｓｆｏｒＤｉａｔｏｍｉｃＣｈａｉｎｗｉｔｈＱｕａｒｔｉｃＳｕｂｓｔｒａｔｅＮｏｎｌｉｎｅａｒｉｔｙＺｈｏｕＧｕａｎｇｈｕｉＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓａｎｄＩｎｓ...

关键词： Diatomic chain Phase plane analysis Nonlinear vibrational modes

The information entropy of a static dilaton black hole

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Science china(physics,Mechanics & Astronomy) 2008年第2期51卷 113-125页

作者： LIU ChengZhou institute of Theoretical physics, Binzhou university, Binzhou 256600, china department of physics, Beijing normal university, Beijing 100875, china 1. institute of Theoretical physics Binzhou University Binzhou 256600 China 2. department of physics Beijing Normal University Beijing 100875 China

In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.

关键词： black hole entropy holographic principle non-commutative quantum field theory event horizon loop quantum gravity