By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-bran...By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ（x）, and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.展开更多
By decomposing the Bogomol＇nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selldual topological term that was ignored all the time in the Bogomol＇nyi self-duality equation due to the improp...By decomposing the Bogomol＇nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selldual topological term that was ignored all the time in the Bogomol＇nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a new self-dual equation that includes the topological term. It is shown that the self-dual vortex just arises from the symmetric phase of the Higgs field φ =0. Using our p-mapping theory, the inner topological structure of the vortex and double vortex is given.展开更多
It is well known that ＇t Hooft-Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, i.e. the so-called ＇t Hooft tensor in three-dimensional space, which has been ge...It is well known that ＇t Hooft-Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, i.e. the so-called ＇t Hooft tensor in three-dimensional space, which has been generalized to all even rank ones. We propose an arbitrary odd rank ＇t Hooft tensor, which universally determines the quantized low-energy boundaries of the even dimensional Georgi-Glashow models under asymptotic conditions. Furthermore, the dual magnetic monopole theory is built up in terms of the J-mapping theory.展开更多
A conservation equation for topological charges of phase singularities （scroll and spiral waves） in excitable media is given. It provides some topological properties of scroll （spiral） waves： for example, the top...A conservation equation for topological charges of phase singularities （scroll and spiral waves） in excitable media is given. It provides some topological properties of scroll （spiral） waves： for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.展开更多
The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological curren...The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.展开更多
Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually fo...Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and can be even linked and knotted. We give a rigorous topological description of knotted vortex filaments. By using the Ф-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments, and using this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.展开更多
Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are diff...Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of 未 function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a 未-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.展开更多
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 wavefunction.The internal symmetry of physical system ...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 wavefunction.The 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.展开更多
In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)...In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)≠0.When J(ø/v)=0,it is shown that there exists the crucial case of branch process.Based on the implicit function theorem and the Taylor expansion,the generation,annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ø-mapping,respectively.展开更多
Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear d...Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear defects are described by the Winding numbers of Ф-mapping which are determined in terms of the Hopf indices and the Brouwer degrees.All the topological linear defects are generated from the zero points of the Ф-mapping.展开更多
By decomposing SU（2） gauge potential in four-dimensional Euclidean SU（2） Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topolog...By decomposing SU（2） gauge potential in four-dimensional Euclidean SU（2） Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.展开更多
By making use of the C-mapping topological current theory, this paper shows that the Gauss Bonnet Chern density （the Euler-Poincare characteristic x（M） density） can be expressed in terms of a smooth vector field ...By making use of the C-mapping topological current theory, this paper shows that the Gauss Bonnet Chern density （the Euler-Poincare characteristic x（M） density） can be expressed in terms of a smooth vector field φ and take the form of δ（φ）, which means that only the zeros of φ contribute to x（M）. This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of p-branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi p-branes.展开更多
In the light of the decomposition of the SU（2） gauge potential for I = 1/2, we obtain the SU（2） Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall ef...In the light of the decomposition of the SU（2） gauge potential for I = 1/2, we obtain the SU（2） Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect （2D FQH） which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU（2） Chern-Simons vortices are generated from the zero points of the two-component wave functions ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of Ф-mapping under the condition that the zero points of field ψ are regular points.展开更多
Based on Duan’s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are diff...Based on Duan’s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of δ function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10475034）.
文摘By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ（x）, and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.
基金Supported by the National Natural Science Foundation under Grant No 10175028, and the Doctorial Education Fund of the Ministry of Education of China under Grant No 20010730007.
文摘By decomposing the Bogomol＇nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selldual topological term that was ignored all the time in the Bogomol＇nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a new self-dual equation that includes the topological term. It is shown that the self-dual vortex just arises from the symmetric phase of the Higgs field φ =0. Using our p-mapping theory, the inner topological structure of the vortex and double vortex is given.
基金Supported by the National Natural Science Foundation of China under Grant No 10175028, and the Doctor Education Fund of Educational Department of China.
文摘It is well known that ＇t Hooft-Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, i.e. the so-called ＇t Hooft tensor in three-dimensional space, which has been generalized to all even rank ones. We propose an arbitrary odd rank ＇t Hooft tensor, which universally determines the quantized low-energy boundaries of the even dimensional Georgi-Glashow models under asymptotic conditions. Furthermore, the dual magnetic monopole theory is built up in terms of the J-mapping theory.
基金Supported by the National Natural Science Foundation of China under Grant No 10675099, the Hong Kong Research Council （RGC）, and the Hong Kong Baptist University Faculty Research Fund （FRG）.
文摘A conservation equation for topological charges of phase singularities （scroll and spiral waves） in excitable media is given. It provides some topological properties of scroll （spiral） waves： for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.
基金Support by the National Natural Science Foundation of China, and Cuiying Programme of Lanzhou University. The authors would like to thank Xin-Hui Zhang, Dong-Hui Xu, and Ran Li for helpful discussions.
文摘The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.
基金Support by the National Natural Science Foundation of China, and Cuiying Programme of Lanzhou University.
文摘Scroll waves exist ubiquitously in three-dimensional excitable media. The rotation centre can be regarded as a topological object called the vortex filament. In three-dimensional space, the vortex filaments usually form closed loops, and can be even linked and knotted. We give a rigorous topological description of knotted vortex filaments. By using the Ф-mapping topological current theory, we rewrite the topological current form of the charge density of vortex filaments, and using this topological current we reveal that the Hopf invariant of vortex filaments is just the sum of the linking and self-linking numbers of the knotted vortex filaments. We think that the precise expression of the Hopf invariant may imply a new topological constraint on knotted vortex filaments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10905026 and 10905027)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090211120030)the Lanzhou Development of Science and Technology Program,China(Grant No.2010-1-129)
文摘Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of 未 function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a 未-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.
基金Supported by the National Natural Science Foundation of China under Grant No.19115021.
文摘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 wavefunction.The 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.
基金Supported by the National Natural Science Foundation of China under Grant No.19775021.
文摘In the light of ø-mapping method and topological current theory,the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J(ø/v)≠0.When J(ø/v)=0,it is shown that there exists the crucial case of branch process.Based on the implicit function theorem and the Taylor expansion,the generation,annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ø-mapping,respectively.
基金Supported by the National Natural Science Foundation of China under Grant No.19775021.
文摘Using Ф-mapping method and topological current theory,we get the topological structure and the topological quantization of topological linear defects and point out that the topological quantum numbers of the linear defects are described by the Winding numbers of Ф-mapping which are determined in terms of the Hopf indices and the Brouwer degrees.All the topological linear defects are generated from the zero points of the Ф-mapping.
文摘By decomposing SU（2） gauge potential in four-dimensional Euclidean SU（2） Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.
基金Project supported by the National Natural Science Foundation of China (Grant No 10475034)
文摘By making use of the C-mapping topological current theory, this paper shows that the Gauss Bonnet Chern density （the Euler-Poincare characteristic x（M） density） can be expressed in terms of a smooth vector field φ and take the form of δ（φ）, which means that only the zeros of φ contribute to x（M）. This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of p-branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi p-branes.
基金Supported by the National Natural Science Foundation of China under the Grant No 10705008.
文摘In the light of the decomposition of the SU（2） gauge potential for I = 1/2, we obtain the SU（2） Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect （2D FQH） which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU（2） Chern-Simons vortices are generated from the zero points of the two-component wave functions ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of Ф-mapping under the condition that the zero points of field ψ are regular points.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10905026 and 10905027)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090211120030)the Lanzhou Development of Science and Technology Program,China(Grant No.2010-1-129)
文摘Based on Duan’s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of δ function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.
