arXiv subjects

Yishi Duan

Publications and source records attributed to Yishi Duan.

At least 19 recordsLinked to original sources

arXiv2005

Topological quantization of self-dual Chern-Simons vortices on Riemann Surfaces

The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and $ϕ$-mapping method. The special form of the gauge potential decomposition is obtained directly from the first of the self-duality equations. Using this decomposition, a rigorous proof of magnetic flux quantization in background curved spacetime is given and the unit magnetic flux in curved spacetime is also found . Furthermore, the precise self-dual vortex equation with topological term is obtained, in which the topological term has always been ignored.

hep-th↗

arXiv2001

Novel Theory for Topological Structure of Vortices in BEC

By making use of the $ϕ$-mapping topological current theory, a novel expression of $\nabla \times \vec{V}$ in BEC is obtained, which reveals the inner topological structure of vortex lines characterized by Hopf indices and Brouwer degrees. This expression is just that formula Landau and Feynman expected to find out long time ago. In the case of superconductivity, the decomposition theory of U(1) gauge potential in terms of the condensate wave function gives a rigorous proof of London assumption, and shows that each vortex line should carry a quantized flux. The $ϕ$-mapping topological current theory of $\nabla \times \vec{V}$ can also gives a precise bifurcation theory of vortex lines in BEC.

cond-mat.mes-hall↗

arXiv1999

A new topological aspect of the arbitrary dimensional topological defects

We present a new generalized topological current in terms of the order parameter field $\vec ϕ$ to describe the arbitrary dimensional topological defects. By virtue of the $% ϕ$-mapping method, we show that the topological defects are generated from the zero points of the order parameter field $\vec ϕ$, and the topological charges of these topological defects are topological quantized in terms of the Hopf indices and Brouwer degrees of $ϕ$-mapping under the condition that the Jacobian $% J(\frac ϕv)\neq 0$. When $J(\frac ϕv)=0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function $\vec ϕ$ but the total charge of the topological defects is still unchanged.

hep-th↗

arXiv1999

The branch process of the cosmic strings

In the light of $ϕ$-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian $J(ϕ/v)\neq0$. When $J(ϕ/v)=0$, 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 $ϕ$-mapping, respectively.

hep-th↗

arXiv1999

Topological current of point defects and its bifurcation

From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution of point defects is also studied. One concludes that there exist crucial cases of branch processes in the evolution of point defects when the Jacobian $D(\frac ϕx)=0$.

hep-th↗

arXiv1999

The General Decomposition Theory of SU(2) Gauge Potential, Topological Structure and Bifurcation of SU(2) Chern Density

By means of the geometric algebra the general decomposition of SU(2) gauge potential on the sphere bundle of a compact and oriented 4-dimensional manifold is given. Using this decomposition theory the SU(2) Chern density has been studied in detail. It shows that the SU(2) Chern density can be expressed in terms of the $δ-$function $δ(ϕ) $. And one can find that the zero points of the vector fields $ϕ$ are essential to the topological properties of a manifold. It is shown that there exists the crucial case of branch process at the zero points. Based on the implicit function theorem and the taylor expansion, the bifurcation of the Chern density is detailed in the neighborhoods of the bifurcation points of $ϕ$. It is pointed out that, since the Chren density is a topological invariant, the sum topological chargers of the branches will remain constant during the bifurcation process.

hep-th↗

arXiv1999

The second Chern class in Spinning System

Topological property in a spinning system should be directly associated with its wavefunction. A complete decomposition formula of SU(2) gauge potential in terms of spinning wavefunction is established rigorously. Based on the $ϕ$-mapping theory and this formula, one proves that the second Chern class is inherent in the spinning system. It is showed that this topological invariant is only determined by the Hopf index and Brouwer degree of the spinning wavefunction.

hep-th↗

arXiv1999

Topological quantum mechanics and the first Chern class

Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological invariant, the first Chern class, is inherent in the Schrödinger system, which is only associated with the Hopf index and Brouwer degree of the wave function. This relationship between the first Chern class and the wave function is the topological source of many topological effects in quantum system.

hep-th↗

arXiv1999

Topological tensor current of $\tilde{p}$-branes in the $ϕ$-mapping theory

We present a new general topological tensor current of $\tilde{p}$-branes by making use of the $ϕ$-mapping theory. It is shown that the current is identically conserved and behave as $δ(\vecϕ),$ and every isolated zero of the vector field $\vecϕ(x)$ corresponds to a `magnetic' $\tilde{p}$-brane. Using this topological current, the generalized Nambu action for multi $\tilde{p}$-branes is given, and the field strength $F$ corresponding to this topological tensor current is obtained. It is also shown that the `magnetic' charges carried by $\tilde{p}$-branes are topologically quantized and labeled by Hopf index and Brouwer degree, the winding number of the $ϕ$-mapping.

hep-th↗

arXiv1999

Decomposition Theory of Spin Connection and Topological Structure of Gauss-Bonnet-Chern Theorem on Manifold With Boundary

The index theorem of Euler-Poincaré characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $ϕ$ and half the total of the projective vector field of $ϕ$ on the boundary equals the Euler-Poincaré characteristic of the manifold. Detailed discussion on the topological structure of the Gauss-Bonnet-Chern theorem on manifold with boundary is given. The Hopf indices and Brouwer degrees label the local structure of the Euler density.

math-ph↗

arXiv1998

Can torsion play a role in angular momentum conservation law?

In Einstein-Cartan theory, by the use of the general Noether theorem, the general covariant angular-momentum conservation law is obtained with the respect to the local Lorentz transformations. The corresponding conservative Noether current is interpreted as the angular momentum tensor of the gravity-matter system including the spin density. It is pointed out that, assuming the tetrad transformation given by eq. (15), torsion tensor can not play a role in the conservation law of angular momentum.

gr-qc↗

arXiv1998

SO(4) Monopole As A New Topological Invariant And Its Topological Structure

By making use of the decomposition theory of gauge potential, the inner structure of SU(2) and SO(4) gauge theory is discussed in detail. We find the SO(4) monopole can be given via projecting the SO(4) gauge field onto an antisymmetric tensor. This projection fix the coset $% SU(2)/U(1)\bigotimes SU(2)/U(1)$ of SO(4) gauge group. The generalized Hopf map is given via a Dirac spinor. Further we prove that this monopole can be consider as a new topological invariant. Which is composed of two monopole structures. Local topological structure of the SO(4) monopole is discussed in detail, which is quantized by winding number. The Hopf indices and Brouwer degree labels the local property of the monopoles.

hep-th↗

arXiv1998

The topological quantization and the branch process of the (k-1)-dimensional topological defects

In the light of $ϕ$-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian $J(ϕ/v) \neq 0$. When $J(ϕ/v)=0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of generalized topological current and find different directions of the bifurcation. The arbitrary dimensional topological defects are found splitting or merging at the degenerate point of field function $\vec ϕ$ but the total charge of the topological defects is still unchanged.

hep-th↗

arXiv1998

The Bifurcation of the Topological Structure in the Sunspot's Electric Topological Current with Locally Gauge-invariant Maxwell-Chern-Simons Term

The topological structure of the electric topological current of the locally gauge invariant Maxwell-Chern-Simons Model and its bifurcation is studied. The electric topological charge is quantized in term of winding number. The Hopf indices and Brouwer degree labeled the local topological structure of the electric topological current. Using $Φ$-mapping method and implicity theory, the electric topological current is found generating or annihilating at the limit points and splitting or merging at the bifurcate points. The total electric charge holds invariant during the evolution.

gr-qc↗

arXiv1998

Strings and the Gauge Theory of Spacetime Defects

we present a new topological invariant to describe the space-time defect which is closely related to torsion tensor in Riemann-Cartan manifold. By virtue of the topological current theory and $ϕ$-mapping method, we show that there must exist many strings objects generated from the zero points of $ϕ$-mapping, and these strings are topological quantized and the topological quantum numbers is the Winding numbers described by the Hopf indices and the Brouwer degrees of the $ϕ$-mapping.

hep-th↗

arXiv1998

The topological quantization and bifurcation of the topological linear defects

In the light of $ϕ$-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that the Jacobian $J(ϕ/v) \neq 0$. When $J(ϕ/v) = 0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of $ϕ$-mapping, respectively.

hep-th↗

arXiv1998

The generation of the (k-1)-dimensional defect objects and their topological quantization

In the light of $ϕ$--mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are investigated. It is pointed out that the topological quantum numbers of the defects are described by the Winding numbers of $ϕ$--mapping which are determined in terms of the Hopf indices and the Brouwer degrees of $ϕ$--mapping. Furthermore, it is shown that all the topological defects are generated from where $\vec ϕ=0$, i.e. from the zero points of the $ϕ$--mapping.

hep-th↗

arXiv1998

The topological structure of the vortices in the O(n) symmetric TDGL model

In the light of $ϕ$--mapping method and topological current theory, the topological structure of the vortex state in TDGL model and the topological quantization of the vortex topological charges are investigated. It is pointed out that the topological charges of the vortices in TDGL model are described by the Winding numbers of $ϕ$--mapping which are determined in terms of the Hopf indices and the Brouwer degrees of $ϕ$--mapping.

hep-th↗