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Topological Structure of Phase Vortex in Resonating Valence Bond Superconductivity

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Communications in Theoretical Physics 2006年第1X期46卷 33-36页

作者： shi Xu-Guang duan yi-shi College of Basic Science and Technology Beijing Forestry University Beijing 100083 China Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

In this paper, based on the Schrfdinger equation and the ψ mapping theory, the accurate expression for the gradient of resonating valence bond superconducting phase Θ^2s is found. The expression of Δ↓Θ^2s is just the velocity flow without considering the coefficient. The curl of Δ↓Θ^2s is where the vortex lies, and has important relation to δ2（ψ） and an important relation to the zero points of resonating valence bond superconducting order parameter ψ. The topological structure of the vortex is characterized by the ψ-mapping topological numbers Hopf-index and Brouwer degrees. The Ginzberg-Landau equation in resonating valence bond state also is discussed in this theory. The magnetic property is discussed also.

关键词： ψ-mapping theory phase vortex GL-equation RVB superconductivity

Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory

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Communications in Theoretical Physics 2005年第3X期44卷 559-562页

作者： duan yi-shi ZHANG Xiu-Ming Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

Based on the decomposition theory of the U（1） gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau （CSGL） theory is studied. We give a new creation mechanism of the statistical gauge potential, Furthermore, making use of the b-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.

关键词： gauge potential decomposition theory topological quantum mechanics

Surface Distribution of Topological Defects on Axisymmetric

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Communications in Theoretical Physics 2006年第2X期46卷 319-322页

作者： SI Tie-Yan duan yi-shi Institute of Theoretical Physics the Chinese Academy of Sciences Beijing 100080 China Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

We propose a general method of deterrnining the distribution of topological defects on axisymmetric surface, and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface： four defects charged with 1/2, two defects charged with ＋1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.

关键词： topolotical defects membrane axisymmetric surface

Generalized Dirichlet Normal Ordering in Open Bosonic Strings

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Communications in Theoretical Physics 2009年第1期51卷 110-114页

作者： CAO Zhen-Bin duan yi-shi Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly discuss how to build up a generalized Dirichlet normal ordered product of open bosonic string embedding operators that satisfies both the equations of motion and the generalized Dirichlet boundary conditions at the quantum level in the presence of an antisymmetric background field, as the generalized Neumann case has already been discussed in the literature. Further, we also give a brief check of the consistency of the theory under the newly introduced normal ordering.

关键词： boundary conditions normal ordering

Integer and Half-Integer Quantization Conditions in Quantum Mechanics

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Chinese Physics Letters 2001年第4期18卷 473-475页

作者： duan yi-shi JIA Duo-Jie Institute of Theoretical Physics Lanzhou UniversityLanzhou 730000

The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor *** internal symmetry of physical system is shown to be sufficient to determine the topological structure in quantum mechanics without taking into account the dynamical details about the interaction.

关键词： interaction. integer symmetry

Self-dual Vortices in Schrdinger-Chern-Simons Model

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Communications in Theoretical Physics 2008年第9期50卷 757-762页

作者： duan yi-shi TIAN Miao ZHANG Xin-Hui Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China School of Mathematics Physics and Software Engineering Lanzhou Jiaotong University Lanzhou 730070 China

By making use of the U（1） gauge potential decomposition theory and the Ф-mapping topological current theory, we investigate the Schroedinger-Chern-Simons model in the thin-film superconductor system and obtain an exact Bogomolny self-dual equation with a topological term. It is revealed that there exist self-dual vortices in the system. We study the inner topological structure of the self-dual vortices and show that their topological charges are topologically quantized and labeled by Hopf indices and Brouwer degrees. Furthermore, the vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field Ф.

关键词： self-dual vortices thin-film superconductors

A New Route to the Interpretation of Hopf Invariant

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Communications in Theoretical Physics 2008年第7期50卷 53-58页

作者： REN Ji-Rong LI Ran duan yi-shi Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current *** main purpose of this paper is to present a new theoretical framework,which can directlygive the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclideanspace R^(2n-1).For the sake of this purpose we introduce a topological tensor current,which can naturally deduce the(n-1)-dimensional topological defect in R^(2n-1) *** these (n-1)-dimensional topological defects are closed orientedsubmanifolds of R^(2n-1),they are just the (n-1)-dimensional *** linking number of these knots is well *** the inner structure of the topological tensor current,the relationship between Hopf invariant and the linkingnumbers of the higher-dimensional knots can be constructed.

关键词： Hopf invariant higher-dimensional knot linking number

Topological Structure of Knotted Vortex Lines in Liquid Crystals

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Communications in Theoretical Physics 2007年第6期47卷 1129-1134页

作者： duan yi-shi ZHAO Li ZHANG Xin-Hui Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.

关键词： knotted vortex lines liquid crystals Chern-Simons action branch processes

Multi-types of Skyrmions in SU（N） Quantum Hall System

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Communications in Theoretical Physics 2005年第2X期44卷 371-374页

作者： LIU Xin duan yi-shi ZHANG Peng-Ming Department of Mathematics University of Queensland QLD 4072 Australia Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China Department of Mathematics Lanzhou University Lanzhou 730000 China

The skyrmions in SU（N） quantum Hall （QH） system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU（N） QH system there can exist （N-1） types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the （N - 1） Cartan subalgebra local bases, we obtain the （N - 1） U（1） electromagnetic field tensors in the SU（N） gauge field of the QH system, and then derive （N - 1） types of skyrmion structures from these U（1） sub-field tensors. Furthermore, in light of the C-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.

关键词： skyrmions quantum hall system topological field theory