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A novel approach to topological defects in a vector order parameter system

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Chinese Physics B 2009年第7期18卷 2901-2904页

作者：任继荣戎树军朱涛 Institute of Theoretical Physics Lanzhou University

Based on Duan＇s topological current theory,we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter *** method shows explicitly the fine topological structure of *** branch processes of defects in the vector order parameter system have also been investigated with this method.

关键词： topological defects order parameter topological current branch processes

topological Aspects of Entropy and Phase Transition of Kerr Black Holest

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Communications in Theoretical Physics 2005年第4X期44卷 631-637页

作者： YANG Guo-Hong YAN Ji-Jiang TIAN Li-Jun DUAN Yi-Shi Department of Physics Shanghai University Shanghai 200444 China Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem, it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime. By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4 for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.

关键词： topological current entropy Kerr black hole Euler characteristic Killing vector field

Knotted topological Phase Singularities of Electromagnetic Field

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Communications in Theoretical Physics 2008年第11期50卷 1071-1076页

作者： REN Ji-Rong ZHU Tao MO Shu-Fan Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

In this paper,knotted objects (RS vortices) in the theory of topological phase singularity in electromagneticfield have been investigated in *** using the Duan's topological current theory,we rewrite the topological currentform of RS vortices and use this topological current we reveal that the Hopf invariant of RS vortices is just the sum ofthe linking and self-linking numbers of the knotted RS ***,the conservation of the Hopf invariant inthe splitting,the mergence and the intersection processes of knotted RS vortices is also discussed.

关键词： knotted optical vortex topological current phase singularity

Evolution of Spiral Waves in Excitable Systems

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Communications in Theoretical Physics 2009年第4期51卷 621-626页

作者： REN Ji-Rong ZHU Tao MO Shu-Fan Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.

关键词： topological current spiral wave bifurcation theory of spiral wave

topological Aspect and Bifurcation of Disclination Lines in Two—Dimensional Liquid Crystals

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Communications in Theoretical Physics 2002年第5期37卷 513-518页

作者： YANGGuo－Hong ZHANGHui 等 DepartmentofPhysics ShanghaiUniversityShanghai200436China DepartmentofChemistry ShanghaiUniversityShanghai200436China

Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topologicalcurrent of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices andBrouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not *** the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of disclination lines arestudied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limitpoint and the different directions of all branch curves at the bifurcation point are calculated with the conservation lawof the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and itwill evolve to the lower strength state through the bifurcation process.

关键词： topological current winding number director field disclination line

Topology of Knotted Optical Vortices

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Communications in Theoretical Physics 2008年第8期50卷 345-348页

作者： REN Ji-Rong ZHU Tao DUAN Yi-Shi Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

Optical vortices as topological objects exist ubiquitously in *** this paper,by making use of the Duan's topological current theory,we investigate the topology in the closed and knotted optical *** topological inner s... 详细信息

关键词： optical vortices knot topology topological current

topological Defects in Liquid Crystal Films

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Communications in Theoretical Physics 2007年第6期47卷 1125-1128页

作者： DUAN Yi-Shi ZHAO Li ZHANG Xin-Hui SI Tie-Yan Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China Institute of Theoretical Physics the Chinese Academy of Sciences Beijing 100080 China

A topological theory of liquid crystal films in the presence of defects is developed based on the Ф-mapping topological current theory. By generalizing the free-energy density in ＂one-constant＂ approximation, a covariant free- energy density is obtained, from which the U（1） gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of Ф-mapping.

关键词： director field free-energy density topological current topological defects winding number

topological quantization of disclination points in three—dimensional liquid crystals

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Chinese Physics B 2002年第5期11卷 415-418页

作者：杨国宏张慧等 DepartmentofPhysics ShanghaiUniversityShanghai200436China DepartmentofChemistry ShanghaiUniversityShanghai200436China

Using the φ-mapping method and topological current theory, we study the inner structure of disclination points inthree-dimensional liquid crystals. By introducing the strength density and the topological current of many disclination points, it is pointed out that the disclination points are determined by the singularities of the general director field and they are topologically quantized by the Hopf indices and Brouwer degrees.

关键词： topological current wrapping number director field disclination point

topological Structure of Disclination Lines in 2-Dimensional Liquid Crystals

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Journal of Shanghai University(English Edition) 2002年第3期6卷 207-210页

作者：张慧杨国宏等 DeparmtentofChemistry CollegeofSciencesShanghaiUniversityShanghai200436China DepartmentofPhysics CollegeofSciencesShanghaiUniversityShanghai200436China

Using  mapping method and topological current theory, the topological structure of disclination lines in 2 dimensional liquid crystals is studied. By introducing the strength density and the topological current of many disclination lines, it is pointed out that the disclination lines are determined by the singulaities of the director field, and topologically quantized by the Hopf indices and Brouwer degrees. Due to the equivalence in physics of the director fields n (x) and n (x) , the Hopf indices can be integers or half integers, representing a generalization of our previous studies of integer Hopf indices.

关键词： topological current winding number director field disclination line.