214 results on '"Yi-Shi Duan"'
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2. Extended Theory of Harmonic Maps Connects General Relativity to Chaos and Quantum Mechanism
- Author
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Yi-Shi Duan and Gang Ren
- Subjects
High Energy Physics - Theory ,extended theory of harmonic maps ,General Mathematics ,General Physics and Astronomy ,FOS: Physical sciences ,Relativistic quantum mechanics ,General Relativity and Quantum Cosmology (gr-qc) ,01 natural sciences ,Classical physics ,General Relativity and Quantum Cosmology ,Article ,Mathematical Sciences ,010305 fluids & plasmas ,Theoretical physics ,Theory of relativity ,Engineering ,Information and Computing Sciences ,0103 physical sciences ,Effective field theory ,Mathematical Physics ,Physics ,Quantum Physics ,Extended harmonic maps ,Applied Mathematics ,Statistical and Nonlinear Physics ,Four-force ,Mathematical Physics (math-ph) ,Nonlinear Sciences - Chaotic Dynamics ,Quantum chaos ,Classical mechanics ,High Energy Physics - Theory (hep-th) ,General relativity ,Problem of time ,chaos equation ,quantum physics ,Quantum gravity ,010307 mathematical physics ,Chaotic Dynamics (nlin.CD) ,Quantum Physics (quant-ph) - Abstract
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement. Here, we showed the early reported extended HM theory that included the general relativity can also be used to recover the classic chaos equations and even the Schrodinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory of physics., Comment: 8 page, no figures
- Published
- 2017
3. REDUCED QUANTUM TOPOLOGICAL TRAJECTORY IN COHERENCE AND DECOHERENCE
- Author
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Yi-Shi Duan and Xuguang Shi
- Subjects
Physics ,Nuclear and High Energy Physics ,medicine.medical_specialty ,Topological degeneracy ,General Physics and Astronomy ,Astronomy and Astrophysics ,Topological dynamics ,Topology ,Topological quantum computer ,Topological entropy in physics ,Symmetry protected topological order ,Classical mechanics ,Quantum mechanics ,medicine ,Topological order ,Quantum algorithm ,Topological quantum number - Abstract
We have studied the topological expression of the reduced quantum trajectory using ϕ-mapping topological current theory and reduced density matrix theory. Moreover, we have proposed a new topological expression called the reduced quantum topological trajectory. Ignoring the coefficients of the winding number, we have found that the expression for the reduced quantum topological trajectory is the same for coherence as it is for decoherence. Under certain conditions, the vorticity of the reduced quantum topological trajectory is a topological invariant.
- Published
- 2011
4. MULTIVORTICES EVOLUTION IN WEAK COUPLED ABJM THEORY
- Author
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Yi-Shi Duan, Yang Li, Yu-Xiao Liu, and Jie Yang
- Subjects
M-theory ,Physics ,Nuclear and High Energy Physics ,Work (thermodynamics) ,Current (mathematics) ,Classical mechanics ,Condensed Matter::Superconductivity ,Astronomy and Astrophysics ,Scattering theory ,Vorticity ,Atomic and Molecular Physics, and Optics ,Vortex - Abstract
Following Auzzi' work (arXiv:0906.2366), where new vortex solution is found in weak coupled ABJM theory, we apply the ϕ-mapping topological current method to this vortex, and find the multivortices solution could be obtained naturally. Also this multivortices solution gives a clue of the possibility for the antivortex existence. Then we continue to investigate the vortices evolution of the solution, and this leads to the multivortices evolution that used to be hard to handle in conventional vortices scattering theory.
- Published
- 2010
5. LOCALIZATION OF MATTERS ON A NON-Z2-SYMMETRIC THICK BRANE
- Author
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Yi-Shi Duan and Jun Liang
- Subjects
Physics ,Nuclear and High Energy Physics ,Zero mode ,Scalar (mathematics) ,Yukawa potential ,General Physics and Astronomy ,Astronomy and Astrophysics ,Spinor field ,Quantum electrodynamics ,Brane cosmology ,Black brane ,Brane ,Scalar field ,Mathematical physics - Abstract
We study localization of various matter fields on a non-Z2-symmetric scalar thick brane in a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. It is shown that, for spin 0 scalar field, the massless zero mode can be normalized on the brane. Spin 1 vector field cannot be normalized on the brane. And there is no spinor field which can be trapped on the brane for the case of no Yukawa-type coupling. By introducing the appropriate Yukawa coupling, the left or right chiral fermionic zero mode can be localized on the brane.
- Published
- 2010
6. TOPOLOGICAL ASPECTS OF THE PROTON VORTEX CLUSTERS IN THE CORE OF A NEUTRON STAR
- Author
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Jun Liang and Yi-Shi Duan
- Subjects
Physics ,Proton ,Topological degeneracy ,Nuclear Theory ,Astronomy and Astrophysics ,Topology ,Topological entropy in physics ,Symmetry protected topological order ,Vortex ,Space and Planetary Science ,Condensed Matter::Superconductivity ,Limit point ,Topological order ,Nuclear Experiment ,Mathematical Physics ,Topological quantum number - Abstract
Based on the ϕ mapping topological current theory, the proton vortex clusters in the core of a neutron star are investigated. We derive rigorously the London equation with topological structure for superconducting protons. We also show that the proton vortices can only stem from the zero points of the vector order parameter. The evolution of the proton vortices is discussed, the proton vortices are found generating or annihilating at the limit points and splitting or merging at the bifurcation points of the vector order parameter, and the total topological charges remain invariant during the evolution.
- Published
- 2009
7. Localization of matters on the bent brane in AdS5 bulk
- Author
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Yi-Shi Duan and Jun Liang
- Subjects
Coupling constant ,Physics ,Nuclear and High Energy Physics ,Zero mode ,Fermionic field ,High Energy Physics::Lattice ,High Energy Physics::Phenomenology ,Yukawa potential ,Massless particle ,General Relativity and Quantum Cosmology ,High Energy Physics::Theory ,symbols.namesake ,Quantum mechanics ,symbols ,Brane ,Scalar field ,Mathematical physics ,Spin-½ - Abstract
We investigate the possibility of localizing various matter fields on a bent AdS 4 ( dS 4 ) thick brane in AdS 5 . For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.
- Published
- 2009
8. Localization of matter and fermion resonances on double walls
- Author
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Jun Liang and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,Zero mode ,Localization of fields ,Fermion resonances ,Fermion ,Massless particle ,Spinor field ,Zero modes ,Quantum mechanics ,Brane cosmology ,Extra dimensions ,Brane ,Scalar field ,Spin-½ - Abstract
We investigate the possibility of localizing various matter fields on the double walls. For spin 0 scalar field, massless zero mode can be normalized on the double walls. However, for spin 1 vector field, the zero mode is not localized on the double walls. In the paper [C.A.S. Almeida, M.M. Ferreira Jr., A.R. Gomes, R. Casana, arXiv:0901.3543 [hep-th]], the authors investigated fermion localization on a Bloch brane, especially, they found fermion resonances on the Bloch brane for both chiralities and related their appearance to branes with internal structure. Inspired by their work, for spin 1/2 spinor field, we focus our attention mainly on the fermion resonances, and also found fermion resonances for both left-handed fermions and right-handed ones on the double walls, which further supports the arguments presented in the paper [C.A.S. Almeida, M.M. Ferreira Jr., A.R. Gomes, R. Casana, arXiv:0901.3543 [hep-th]].
- Published
- 2009
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9. The Generalization of Chern-Simons Current and the Topological Tensor Current of p-Branes
- Author
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Yi-Shi Duan, Jie Yang, and Yu-Xiao Liu
- Subjects
High Energy Physics::Theory ,Hamiltonian lattice gauge theory ,Topological quantum field theory ,Physics and Astronomy (miscellaneous) ,Topological algebra ,General Mathematics ,Chern–Simons theory ,Topological order ,Topology ,Topological entropy in physics ,Symmetry protected topological order ,Topological quantum number ,Mathematics - Abstract
To make the gauge field theory foundation of the topological current of p-branes introduced in our previous work, we present a novel topological tensor current in SO(N) gauge field theory. This non-Abelian gauge field tensor current is the straightforward generalization of the Chern-Simons topological current of strings. By making use of the SO(N) gauge potential decomposition theory and the φ-mapping topological current theory, it is proved that the p-brane is created at every isolated zero of the Clifford vector field $\overrightarrow{\phi }(x)$ and the charges carried by p-branes are topologically quantized and labelled by the winding number of the φ-mapping.
- Published
- 2009
10. EXTRA DIMENSIONS WITH NONTRIVIAL TORSION AND SPINS OF COSMIC STRINGS
- Author
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Zhen-Bin Cao and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,Spacetime ,Spins ,General relativity ,General Physics and Astronomy ,Torsion (mechanics) ,Astronomy and Astrophysics ,Type I string theory ,Cosmic string ,symbols.namesake ,Extra dimensions ,Theoretical physics ,Classical mechanics ,symbols ,Einstein - Abstract
As two generalizations of Einstein's general relativity, the nontrivial spacetime torsion and the compact extra dimensions have been largely studied in the literature. In this paper, by combining a torsioned Kaluza–Klein scheme and the field-theory cosmic string theory, we discuss that a higher-dimensional torsion component can be expressed in terms of the usual four-dimensional field strength two-form, and this torsion form can then get trapped into the cores of the cosmic strings and further relate to the intrinsic spins of the strings.
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- 2009
11. TOPOLOGICAL STRUCTURE OF VORTEX LINES OF QUANTUM ELECTRON PLASMAS IN THREE-DIMENSIONAL SPACE
- Author
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Yi-Shi Duan and Xuguang Shi
- Subjects
Physics ,Condensed matter physics ,Topological degeneracy ,Statistical and Nonlinear Physics ,Vorticity ,Condensed Matter Physics ,Space (mathematics) ,Topology ,Symmetry protected topological order ,Vortex ,Condensed Matter::Superconductivity ,Quantum mechanics ,Topological order ,Wave function ,Topological quantum number - Abstract
The topological properties of quantum electron plasmas in three-dimensional space are presented. Starting from ϕ-mapping topological current theory, the vortex lines are just at the core of wave function obtained. It is shown that the vorticity of the vortex can be expressed by the Hopf index and the Brouwer degree. We find that the vortex lines are unstable in some conditions and the evolution of vortex lines at the bifurcation points is given.
- Published
- 2009
12. OPEN STRING IN pp-WAVE BACKGROUND WITH B-FIELD
- Author
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Yi-Shi Duan and Zhen-Bin Cao
- Subjects
Heterotic string theory ,Physics ,Nuclear and High Energy Physics ,Compactification (physics) ,General Physics and Astronomy ,Astronomy and Astrophysics ,String field theory ,Type I string theory ,Relationship between string theory and quantum field theory ,High Energy Physics::Theory ,Non-critical string theory ,Classical mechanics ,String cosmology ,String duality ,Mathematical physics - Abstract
The open string ending on a flat D-brane in the pp-wave background with a constant B-field is exactly solvable but will be controlled by a more mass parameter. In this paper we mainly quantize this open string theory canonically by employing the Faddeev–Jackiw symplectic quantization procedure, and find that the phase space of the string coordinate and canonical momentum becomes fully noncummutative, consistent with the results obtained previously.
- Published
- 2009
13. TOPOLOGICAL SOLUTION OF BOHMIAN QUANTUM MECHANICS
- Author
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Xuguang Shi, Ming Yu, and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,Pilot wave ,World line ,Topological degeneracy ,General Physics and Astronomy ,Astronomy and Astrophysics ,Topology ,Topological entropy in physics ,Schrödinger equation ,symbols.namesake ,Classical mechanics ,Bifurcation theory ,Quantum mechanics ,symbols ,Topological order ,Topological quantum number ,Mathematical physics - Abstract
The topological solutions of the De Broglie–Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ϕ-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.
- Published
- 2009
14. CANONICAL ANALYSIS OF NONCOMMUTATIVITY OF OPEN BOSONIC STRINGS
- Author
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Yi-Shi Duan and Zhen-Bin Cao
- Subjects
Physics ,Nuclear and High Energy Physics ,General Physics and Astronomy ,Boundary conformal field theory ,Astronomy and Astrophysics ,String field theory ,Noncommutative geometry ,High Energy Physics::Theory ,Non-critical string theory ,symbols.namesake ,Poisson bracket ,Antisymmetric tensor ,Dirichlet boundary condition ,Quantum mechanics ,symbols ,D-brane ,Mathematical physics - Abstract
Generally, in the presence of an antisymmetric tensor background field, the open string moving with mixed Neumann and Dirichlet boundary conditions will make the spacetime coordinates noncommutative. In this paper, comparing to the flat and static D-brane case studied in the literature, we first generalize the D-branes to be dynamical. And then by using the Hamiltonian approach, through a calculation of the classical Poisson brackets among the Fourier mode components of the string embedding coordinates and a consistent quantization procedure, we show that the spacetime coordinates of the string endpoints in the directions parallel and perpendicular to the D-branes both become noncommutative.
- Published
- 2009
15. Generalized Dirichlet Normal Ordering in Open Bosonic Strings
- Author
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Zhen-Bin Cao and Yi-Shi Duan
- Subjects
High Energy Physics - Theory ,Physics ,Physics and Astronomy (miscellaneous) ,Antisymmetric relation ,FOS: Physical sciences ,Equations of motion ,String theory ,String (physics) ,Noncommutative geometry ,symbols.namesake ,High Energy Physics - Theory (hep-th) ,Antisymmetric tensor ,Dirichlet boundary condition ,symbols ,Boundary value problem ,Mathematical physics - Abstract
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., 12 pages, no figures
- Published
- 2009
16. Inner structure of Spinc(4) gauge potential on 4-dimensional manifolds
- Author
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Wen-Li Yang, Yi-Shi Duan, Yao-Zhong Zhang, and Xin Liu
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Instanton ,Spinor ,Spectral theory ,Spinor field ,High Energy Physics::Lattice ,General Physics and Astronomy ,Lambda ,Laplace operator ,Vacuum expectation value ,Mathematical physics ,Spin-½ - Abstract
The decomposition of $Spin^{c}(4)$ gauge potential in terms of the Dirac 4% -spinor is investigated, where an important characterizing equation $\Delta A_{\mu}=-\lambda A_{\mu}$ has been discovered. Here $\lambda $ is the vacuum expectation value of the spinor field, $\lambda =\Vert \Phi \Vert ^{2}$, and $A_{\mu}$ the twisting U(1) potential. It is found that when $\lambda $ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.
- Published
- 2008
17. SELF-DUAL VORTICES IN THE ABELIAN CHERN–SIMONS MODEL WITH TWO COMPLEX SCALAR FIELDS
- Author
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Yi-Shi Duan, Yu-Xiao Liu, and Li-Da Zhang
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Angular momentum ,Scalar (mathematics) ,Chern–Simons theory ,FOS: Physical sciences ,General Physics and Astronomy ,Astronomy and Astrophysics ,Magnetic flux ,Vortex ,High Energy Physics - Theory (hep-th) ,Abelian group ,Scalar field ,Mathematical physics - Abstract
Making use of $\phi$-mapping topological current method, we discuss the self-dual vortices in the Abelian Chern-Simons model with two complex scalar fields. For each scalar field, an exact nontrivial equation with a topological term which is missing in many references is derived analytically. The general angular momentum is obtained. The magnetic flux which relates the two scalar fields is calculated. Furthermore, we investigate the vortex evolution processes, and find that because of the present of the vortex molecule, these evolution processes is more complicated than the vortex evolution processes in the corresponding single scalar field model., Comment: 9 pages, no figures
- Published
- 2008
18. A NEW DESCRIPTION OF COSMIC STRINGS IN BRANE WORLD SCENARIO
- Author
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Yi-Shi Duan, Li-Da Zhang, and Yu-Xiao Liu
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Astrophysics::High Energy Astrophysical Phenomena ,Astrophysics::Instrumentation and Methods for Astrophysics ,Structure (category theory) ,FOS: Physical sciences ,General Physics and Astronomy ,Astronomy and Astrophysics ,Charge (physics) ,Astrophysics::Cosmology and Extragalactic Astrophysics ,Gauge (firearms) ,Magnetic flux ,Cosmic string ,High Energy Physics::Theory ,Theoretical physics ,High Energy Physics - Theory (hep-th) ,Higgs boson ,Brane ,Abelian group - Abstract
In the light of $\phi$-mapping topological current theory, the structure of cosmic strings are obtained from the Abelian Higgs model, which is an effective description to the brane world cosmic string system. In this topological description of the cosmic string, combining the result of decomposition of U(1) gauge potential, we analytically reach the familiar conclusions that in the brane world scenario the magnetic flux of the cosmic string is quantized and the RR charge of it is screened., Comment: 8 pages, no figures
- Published
- 2008
19. GENERAL SPHERICAL SYMMETRY SOLUTION TO EINSTEIN EQUATIONS AND NEWTONIAN GRAVITY MODIFICATION AT SMALL LENGTH SCALE
- Author
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Yi-Shi Duan and Miao Tian
- Subjects
Physics ,Length scale ,Nuclear and High Energy Physics ,Gravity (chemistry) ,Astronomy and Astrophysics ,Coordinate conditions ,Atomic and Molecular Physics, and Optics ,Fock space ,Gravitation ,General Relativity and Quantum Cosmology ,Classical mechanics ,Schwarzschild metric ,Deriving the Schwarzschild solution ,Circular symmetry ,Mathematical physics - Abstract
In this paper, we first we present a general spherical symmetry solution, independent of any coordinate condition, to the Einstein equations. By using this solution, we obtain different cases in different coordinate conditions, such as Schwarzschild solution, Fock solution, which have different forms of f(r). Then, we obtain a modified formula with respect to f(r) of the Newtonian gravity. This formula may describe the gravity at small length scale.
- Published
- 2008
20. DECOMPOSITION OF SU(2) CONNECTION AND KNOT STRUCTURE IN SKYRME–FADDEEV MODEL
- Author
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Ran Li, Ji-Rong Ren, and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,Topological quantum field theory ,Quantum invariant ,Astronomy and Astrophysics ,Atomic and Molecular Physics, and Optics ,Finite type invariant ,Hopf invariant ,Hamiltonian lattice gauge theory ,Knot invariant ,Quantum electrodynamics ,Gauge theory ,Topological quantum number ,Mathematical physics - Abstract
In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simple proposal. We also obtain the action of Skyrme–Faddeev model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. Then, the knot structure in Skyrme–Faddeev model is discussed in terms of the so-called ϕ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of ϕ-mapping, naturally. At last, we briefly discussed the topological invariant–Hopf invariant which describes the topology of these knots. It is shown that Hopf invariant is the total number of all the linking numbers and self-linking numbers of these knots.
- Published
- 2008
21. ENERGY–MOMENTUM FOR RANDALL–SUNDRUM MODELS
- Author
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Yong-Qiang Wang, Yi-Shi Duan, Yu-Xiao Liu, and Li-Jie Zhang
- Subjects
Physics ,Physics::General Physics ,Nuclear and High Energy Physics ,Conservation law ,Current (mathematics) ,Superpotential ,FOS: Physical sciences ,General Physics and Astronomy ,Astronomy and Astrophysics ,Energy–momentum relation ,General Relativity and Quantum Cosmology (gr-qc) ,General Relativity and Quantum Cosmology ,Momentum ,symbols.namesake ,symbols ,Brane ,Planck ,Energy (signal processing) ,Mathematical physics - Abstract
We investigate the conservation law of energy-momentum for Randall-Sundrum models by the general displacement transform. The energy-momentum current has a superpotential and are therefore identically conserved. It is shown that for Randall-Sundrum solution, the momentum vanishes and most of the bulk energy is localized near the Planck brane. The energy density is $\epsilon = \epsilon_0 e^{-3k \mid y \mid}$., Comment: 13 pages, no figures, v4: introduction and new conclusion added, v5: 11 pages, title changed and references added, accepted by Mod. Phys. Lett. A
- Published
- 2008
22. Topological Properties of Spatial Coherence Function
- Author
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Ji-Rong Ren, Yi-Shi Duan, and Tao Zhu
- Subjects
Physics ,Spatial coherence ,FOS: Physical sciences ,General Physics and Astronomy ,Coherence (signal processing) ,Flux quantization ,Phase singularity ,Topology ,Physics - Optics ,Optics (physics.optics) ,Vortex - Abstract
Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by 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., Comment: 9 pages
- Published
- 2008
23. TOPOLOGICAL ZERO-THICKNESS COSMIC STRINGS
- Author
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Zhen-Bin Cao and Yi-Shi Duan
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Current (mathematics) ,High Energy Physics::Lattice ,High Energy Physics::Phenomenology ,FOS: Physical sciences ,General Physics and Astronomy ,Astronomy and Astrophysics ,Gauge (firearms) ,Topology ,Cosmology ,Cosmic string ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Limit (mathematics) ,Gauge theory ,Tensor ,Effective action - Abstract
In this paper, based on the gauge potential decomposition and the $\phi-$mapping theories, we study the topological structures and properties of the cosmic strings that arise in the Abelian-Higgs gauge theory in the zero-thickness limit. After a detailed discussion, we conclude that the topological tensor current introduced in our model is a better and more basic starting point than the generally used Nambu-Goto effective action for studying cosmic strings., Comment: 10 pages, no figures
- Published
- 2007
24. TOPOLOGICAL OBJECTS IN THE O(3) NONLINEAR SIGMA MODEL
- Author
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Yi-Shi Duan, Peng-Ming Zhang, Shao-Feng Wu, and Xi-Guo Lee
- Subjects
Physics ,Nuclear and High Energy Physics ,medicine.medical_specialty ,Topological quantum field theory ,Topological algebra ,Topological degeneracy ,General Physics and Astronomy ,Astronomy and Astrophysics ,Topological dynamics ,Topology ,Topological entropy in physics ,Symmetry protected topological order ,medicine ,Topological order ,Topological quantum number - Abstract
We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2+1)-dimensional spacetime with the CP1 field. Furthermore, we show that there are three kinds of topological defects–vortex lines, point defects and knot exist in the (3+1)-dimensional model, and their topological charges, locations and motions are determined by the ϕ-mapping topological current theory.
- Published
- 2007
25. FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND ON A SPHERE
- Author
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Li Zhao, Li-Jie Zhang, Yu-Xiao Liu, and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,High Energy Physics::Lattice ,Riemann surface ,Zero (complex analysis) ,Astronomy and Astrophysics ,Fermion ,Dirac operator ,Atomic and Molecular Physics, and Optics ,Vortex ,symbols.namesake ,Classical mechanics ,Dirac equation ,symbols ,Higgs boson ,Large extra dimension ,Mathematical physics - Abstract
We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in 5+1 dimensions. Using the generalized Abelian Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra sphere and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a sphere in two simple cases are obtained.
- Published
- 2007
26. Fermion absorption cross section and topology of spherically symmetric black holes
- Author
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Zhen-Bin Cao, Yu-Xiao Liu, Li Zhao, and Yi-Shi Duan
- Subjects
High Energy Physics - Theory ,Physics ,Nuclear and High Energy Physics ,Quantum field theory in curved spacetime ,Absorption cross section ,FOS: Physical sciences ,Fermion ,Topology ,General Relativity and Quantum Cosmology ,symbols.namesake ,Killing vector field ,High Energy Physics - Theory (hep-th) ,Euler characteristic ,Quantum mechanics ,symbols ,Vector field ,Gravitational singularity ,Circular symmetry - Abstract
In 1997, Liberati and Pollifrone in Phys. Rev. D56 (1997) 6458 (hep-th/9708014) achieved a new formulation of the Bekenstein-Hawking formula, where the entropy and the Euler characteristic are related by $S=\chi A/8$. In this work we present a relation between the low-energy absorption cross section for minimally coupled fermions and the Euler characteristic of (3+1)-dimensional spherically symmetric black holes, i.e. $\sigma =\chi g_h^{-1}A$. Based on the relation, using the Gauss--Bonnet--Chern theorem and the $\phi$-mapping method, an absorption cross section density is introduced to describe the topology of the absorption cross section. It is shown that the absorption cross section and its density are determined by the singularities of the timelike Killing vector field of the spacetime and these singularities carry the topological numbers, Hopf indices and Brouwer degrees, naturally., Comment: 16 pages, no figures, accepted by Phys. Lett. B
- Published
- 2007
27. Vector and Spinor Decomposition of SU(2) Gauge Potential, Their Equivalence, and Knot Structure in SU(2) Chern–Simons Theory
- Author
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Ran Li, Ji-rong Ren, and Yi-Shi Duan
- Subjects
High Energy Physics - Theory ,Physics ,Spinor ,Physics and Astronomy (miscellaneous) ,Sigma model ,Chern–Simons theory ,FOS: Physical sciences ,Vector decomposition ,Invariant (physics) ,High Energy Physics::Theory ,High Energy Physics - Theory (hep-th) ,Gauge theory ,Topological quantum number ,Special unitary group ,Mathematical physics - Abstract
In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the $\phi$--mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping., Comment: 10 pages, ni figure
- Published
- 2007
28. TOPOLOGICAL STRUCTURE AND EVOLUTION OF SPACE–TIME DISLOCATIONS AND DISCLINATIONS
- Author
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Yi-Shi Duan and Li Zhao
- Subjects
Physics ,Nuclear and High Energy Physics ,medicine.medical_specialty ,Topological degeneracy ,Astronomy and Astrophysics ,Topological dynamics ,Disclination ,Topology ,Topological entropy in physics ,Symmetry protected topological order ,Atomic and Molecular Physics, and Optics ,Classical mechanics ,Limit point ,medicine ,Topological order ,Topological quantum number - Abstract
By making use of the gauge potential decomposition theory and ϕ-mapping theory, the topological structure and the topological quantization of dislocations and disclinations are studied in the framework of Riemann–Cartan space–time manifold. The evolution of dislocation strings and disclination points is also studied from the topological properties of the order parameter field. The dislocations and disclinations are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the order parameter field.
- Published
- 2007
29. Topological vortices in a two-gap superconductor
- Author
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Li Zhao, Xin-Hui Zhang, and Yi-Shi Duan
- Subjects
Physics ,London equations ,Flux pumping ,Flux pinning ,Condensed matter physics ,Meissner effect ,Condensed Matter::Superconductivity ,Quantum mechanics ,Magnetic flux quantum ,London penetration depth ,Quantum vortex ,General Physics and Astronomy ,Type-II superconductor - Abstract
Based on the ϕ-mapping theory, we derive a new rigorous equation describing the distribution of the magnetic field for vortices in a two-gap superconductor, of which the so-called modified London equation is just a special case in a one-flavor limit. We explicitly investigate the London penetration depth, the Meissner and mixed states and Josephson effect. A magnetic flux quantization condition for vortices in a two-gap superconductor is also derived, from which it follows that in a two-gap superconductor there exist vortices which carry an arbitrary fraction of magnetic flux quantum. The branch processes during the evolution of the vortices in a two-gap superconductor are discussed.
- Published
- 2006
30. MAGNETIC BRANES FROM GENERALIZED 't HOOFT TENSOR
- Author
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Yi-Shi Duan and Shao-Feng Wu
- Subjects
Physics ,Nuclear and High Energy Physics ,Rank (linear algebra) ,High Energy Physics::Lattice ,Dirac (video compression format) ,High Energy Physics::Phenomenology ,Magnetic monopole ,General Physics and Astronomy ,Astronomy and Astrophysics ,High Energy Physics::Theory ,Low energy ,Kernel method ,3d space ,Quantum electrodynamics ,Brane cosmology ,Tensor ,Mathematical physics - Abstract
't Hooft–Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank tensor, the so-called 't Hooft tensor in 3D space. Based on the Chern kernel method, we propose the arbitrary rank 't Hooft tensors, which universally determine the quantized low energy boundaries of generalized Georgi–Glashow models under asymptotic conditions. Furthermore, the dual magnetic branes theory is built up in terms of ϕ-mapping theory.
- Published
- 2006
31. Knotlike χ disclinations in the cholesteric liquid crystals
- Author
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Yi-Shi Duan, Hong Zhang, and Peng-ming Zhang
- Subjects
Statistics and Probability ,Physics ,Condensed matter physics ,Degree (graph theory) ,Quantitative Biology::Tissues and Organs ,Structure (category theory) ,Order (ring theory) ,Statistical and Nonlinear Physics ,Geometry ,Disclination ,Condensed Matter::Soft Condensed Matter ,Hopf invariant ,Liquid crystal ,Physics::Atomic and Molecular Clusters - Abstract
We investigate the topological properties of N ( N ⩾ 1 ) disclination lines in cholesteric liquid crystals. The topological structure of N disclination lines is obtained with the Hopf index and Brouwer degree. Furthermore, the knotted χ disclination loops is proposed with the Hopf invariant. And we consider the stability of such configuration based on the higher order interaction. At last, the evolution of the disclinations is discussed.
- Published
- 2006
32. KNOTTED SELF-DUAL VORTEX IN GENERALIZED ABELIAN CHERN–SIMONS HIGGS FIELD
- Author
-
Yi-Shi Duan, Yong-Qiang Wang, Wojun Zhong, and Tieyan Si
- Subjects
Physics ,Nuclear and High Energy Physics ,Topological quantum field theory ,Spontaneous symmetry breaking ,Chern–Simons theory ,Astronomy and Astrophysics ,Atomic and Molecular Physics, and Optics ,Vortex ,High Energy Physics::Theory ,Higgs field ,Quantum mechanics ,Higgs boson ,Abelian group ,Topological quantum number ,Mathematical physics - Abstract
Based on the Bogomol'nyi self-dual equation in the Abelian Chern–Simons Higgs model, we find a self-dual topological term which 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 generalized self-dual equation for the first time which unified the topological term and nontopological term in (2+1) space–time. It is shown that the self-dual vortex just arise from the symmetric phase of the Higgs field ϕ = 0, this provides a deep insight into the spontaneous symmetry breaking mechanism. When generalizing this model into (3+1) space–time, we show that the topological number on a family of knotted vortex are just the sum of linking number and self-linking number. We also find this topological charge is conserved during the splitting, the mergence and the intersection processes of knotted vortex lines.
- Published
- 2006
33. A NOVEL THEORY OF ELECTROWEAK INSTANTONS
- Author
-
Tieyan Si and Yi-Shi Duan
- Subjects
Physics ,Nuclear and High Energy Physics ,Instanton ,Particle physics ,Topological quantum field theory ,High Energy Physics::Lattice ,High Energy Physics::Phenomenology ,Electroweak interaction ,Phase (waves) ,Structure (category theory) ,General Physics and Astronomy ,Gravitational instanton ,Astronomy and Astrophysics ,BPST instanton ,High Energy Physics::Theory ,Higgs field ,Theoretical physics - Abstract
Using ϕ-mapping topological current theory and the expansion theory of the δ-function, we found a more exact expression of conventional instanton and multi-instanton. We established a novel approach to instanton. It is found that the instantons arise from the symmetric phase of the Higgs field ϕ=0, the fine topological structure of the instanton number is also given.
- Published
- 2005
34. Topological Aspects of Entropy and Phase Transition of Kerr Black Holes
- Author
-
Li-Jun Tian, Guo-Hong Yang, Yi-Shi Duan, and Ji-Jiang Yan
- Subjects
Physics ,Phase transition ,Angular momentum ,Physics and Astronomy (miscellaneous) ,Spacetime ,Event horizon ,Astrophysics::High Energy Astrophysical Phenomena ,Cauchy horizon ,Topology ,General Relativity and Quantum Cosmology ,symbols.namesake ,Killing vector field ,Euler characteristic ,Quantum mechanics ,symbols ,Gravitational singularity ,Mathematical physics - Abstract
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.
- Published
- 2005
35. Inner Structure of Statistical Gauge Potential in Chern–Simons–Ginzburg–Landau Theory
- Author
-
Xiu-Ming Zhang and Yi-Shi Duan
- Subjects
Physics ,High Energy Physics::Theory ,Hamiltonian lattice gauge theory ,Quantum gauge theory ,Physics and Astronomy (miscellaneous) ,Chern–Simons theory ,Structure (category theory) ,Ginzburg–Landau theory ,Gauge (firearms) ,Gauge anomaly ,BRST quantization ,Mathematical physics - Abstract
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 -mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.
- Published
- 2005
36. Various topological excitations in the SO(4) gauge field in higher dimensions
- Author
-
Li-Bin Fu, Yi-Shi Duan, Yao-Zhong Zhang, and Xin Liu
- Subjects
Physics ,Instanton ,High Energy Physics::Lattice ,General Physics and Astronomy ,Topological order ,Gauge theory ,Quantum Hall effect ,Quantum field theory ,Topology ,Symmetry protected topological order ,Topological entropy in physics ,Topological quantum number - Abstract
Following the original analysis Of Zhang and Hu for the 4-dimensional generalization of Quantum Hall effect, there has been much work from different viewpoints on the higher dimensional condensed matter systems. In this paper, we discuss three kinds of topological excitations in the SO(4) gauge field of condensed matter systems in 4-dimension-the instantons and anti-instantons, the 't Hooft-Polyakov monopoles, and the 2-membranes. Using the phi-mapping topological theory, it is revealed that there are 4-, 3-, and 2-dimensional topological currents inhering in the SO (4) gauge field, and the above three kinds of excitations can be directly and explicitly derived from these three kinds of currents, respectively. Moreover, it is shown that the topological charges of these excitations are characterized by the Hopf indices and Brouwer degrees of phi-mapping. (c) 2005 Elsevier Inc. All rights reserved.
- Published
- 2005
37. Multi-types of Skyrmions in SU( N ) Quantum Hall System
- Author
-
Yi-Shi Duan, Peng-Ming Zhang, and Xin Liu
- Subjects
Electromagnetic field ,Physics ,Topological quantum field theory ,Physics and Astronomy (miscellaneous) ,Skyrmion ,High Energy Physics::Phenomenology ,Cartan subalgebra ,Gauge theory ,Quantum Hall effect ,Abelian group ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,Mathematical physics ,Spin-½ - Abstract
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 phi-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.
- Published
- 2005
38. KNOTS IN THE NON-ABELIAN CHERN–SIMONS THEORY
- Author
-
Yi-Shi Duan, Xin Liu, and Peng-Ming Zhang
- Subjects
Physics ,Nuclear and High Energy Physics ,Topological quantum field theory ,Spinor ,Chern–Simons theory ,General Physics and Astronomy ,Astronomy and Astrophysics ,Knot theory ,High Energy Physics::Theory ,Knot (unit) ,Quantum electrodynamics ,Algebra representation ,Abelian group ,Mathematical physics ,Chern–Simons form - Abstract
We employ a spinor decomposition of SU (2) connection to study the Chern–Simons form. Our results show that the SU (2) Chern–Simons action yields the link invariants. Then the structure of the knots is discussed with the ϕ-mapping theory.
- Published
- 2004
39. Spinor field realizations of non-critical strings
- Author
-
Yu-Xiao Liu, Yi-Shi Duan, and Li-Da Zhang
- Subjects
Physics ,High Energy Physics::Theory ,Nuclear and High Energy Physics ,Nilpotent ,Non critical ,Spinor ,Spinor field ,Quantum electrodynamics ,Realization (systems) ,BRST quantization ,Mathematical physics - Abstract
In this paper, we construct the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) charges of spinor non-critical W-2,W-s strings. The cases of s = 3, 4 are discussed in detail, and spinor realization for s = 4 is given explicitly. The BRST charges are graded. (C) 2004 Elsevier B.V. All rights reserved.
- Published
- 2004
40. Knot-like Mermin-Ho vortices in the superfluid 3He–A
- Author
-
Cheng-kui Zhong, Xin Liu, Yi-Shi Duan, and Peng-Ming Zhang
- Subjects
Condensed Matter::Quantum Gases ,Physics ,General Physics and Astronomy ,Linking number ,Mathematics::Geometric Topology ,Vortex ,Knot theory ,Finite type invariant ,Superfluidity ,Hopf invariant ,symbols.namesake ,Knot (unit) ,Quantum mechanics ,symbols ,Abelian group ,Mathematical physics - Abstract
We study the topological properties of knots in superfluid 3 He–A. The decomposition of SO (3) connection and its Abelian projection is presented. The topological structure of Mermin-Ho vortices is obtained with the Abelian projection from the viewpoint of φ -mapping theory. Furthermore, it is shown that the linking number of the knot-like Mermin-Ho vortices can be described with the Hopf invariant. At last, the evolution of the knots is discussed.
- Published
- 2004
41. Knotlike vortex lines in spinor BEC
- Author
-
Xin Liu, Jie Yang, and Yi-Shi Duan
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Knot (unit) ,Spinor ,Quantum mechanics ,General Physics and Astronomy ,Quantum number ,Vortex ,Mathematical physics - Abstract
In this paper the knotlike vortex lines in spinor Bose–Einstein condensates are studied. First it is shown that there are vortex line structures existing in spinor BEC, then we emphasize on the knotlike configurations and study the Faddeev–Niemi (F–N) model to discuss the topology of knots. The important meaning of F–N knot quantum number has been revealed: this number is just the total sum of all the self-linking and linking numbers of the knots family, and it is preserved in the splitting, the mergence and the intersection processes of knotlike vortex lines in spinor BEC.
- Published
- 2004
42. ϕ-MAPPING TOPOLOGICAL THEORY IN TWO-GAP SUPERCONDUCTOR
- Author
-
Xuguang Shi and Yi-Shi Duan
- Subjects
Superconductivity ,Curl (mathematics) ,Physics ,Statistical and Nonlinear Physics ,Vorticity ,Condensed Matter Physics ,Symmetry protected topological order ,Topological entropy in physics ,Vortex ,Theoretical physics ,Classical mechanics ,Condensed Matter::Superconductivity ,Topological order ,Topological quantum number - Abstract
In this paper, the topological structure of the two-gap superconductor is discussed in detail based on the ϕ-mapping theory. The expression of the vorticity ∇×V of the composite vortex is given and the relation between the vorticity and the magnetic field which is carried by the composite vortex is discussed. The curl of velocity ∇×V has important relation to δ2(ϕ) or we can say that ∇×V has an important relation to the zero points of ϕ. The inner structure of the topological current is characterized by the ϕ-mapping topological numbers Hopf-index and Brouwer degrees.
- Published
- 2004
43. DECOMPOSITION OF THE SEMI-SIMPLE GROUP CONNECTION AND COSMIC STRINGS IN THE LORENTZ SPACETIME
- Author
-
Ji-Rong Ren, Yi-Shi Duan, and Peng-Ming Zhang
- Subjects
Physics ,Nuclear and High Energy Physics ,Spacetime ,Group (mathematics) ,Lorentz transformation ,Cartan formalism ,General Physics and Astronomy ,Astronomy and Astrophysics ,Cosmic string ,High Energy Physics::Theory ,Non-critical string theory ,Theoretical physics ,symbols.namesake ,Quantum mechanics ,symbols ,Gauge theory ,Abelian group - Abstract
In a previous paper, we addressed the method of Abelian decomposition to the case of SU (N) Yang–Mills theory. Here, we extend the decomposition method further to the general case. With the Cartan–Weyl basis we decompose semisimple group connection and discuss the SO(3,1) group in particular. In terms of the vierbein projection, we propose two two-forms as the U(1) gauge fields in the SO(3,1) gauge theory and show that these two-forms are just the different cosmic string tensors. Meanwhile, these two-forms indicate that the cosmic strings appear naturally in the Lorentz spacetime, i.e. the torsion in the Riemann–Cartan spacetime is not necessary for the cosmic strings.
- Published
- 2004
44. Velocity field vortices and Mermin-Ho vortices in two-component spinor BEC
- Author
-
Hong Zhang, Xin Liu, and Yi-Shi Duan
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Spinor ,Component (thermodynamics) ,Condensed Matter::Superconductivity ,Quantum mechanics ,Current theory ,Zero (complex analysis) ,General Physics and Astronomy ,Order (ring theory) ,Vector field ,Vortex - Abstract
In light of the φ-mapping topological current theory, two important vortex structures in two-component spinor BEC—the velocity field vortices and the Mermin-Ho vortices are discussed. It is revealed that these two different kinds of vortices are created respectively from the zero points of two different order parameter configurations in the condensates, and both their topological charges, locations and motions can be determined by the φ-mapping theory.
- Published
- 2003
45. THE ORDER PARAMETER FIELD FOR COSMIC STRING, INFLATION AND DARK ENERGY
- Author
-
Peng-Ming Zhang, Li-Ming Cao, and Yi-Shi Duan
- Subjects
Physics ,Inflation (cosmology) ,Nuclear and High Energy Physics ,Particle physics ,Scalar field dark matter ,General Physics and Astronomy ,Astronomy and Astrophysics ,Astrophysics::Cosmology and Extragalactic Astrophysics ,Inflaton ,General Relativity and Quantum Cosmology ,Thermodynamics of the universe ,De Sitter universe ,Dark energy ,Scalar field ,Computer Science::Databases ,Dark fluid - Abstract
We present a whole frame for the cosmic strings, inflation and dark energy with the complex scalar field which can be regarded as the order parameter of our universe. One can find that the comic strings emerge in the zeros of the complex scalar field in the early universe. And with the evolution of complex scalar field, inflation and dark energy can be understood in this frame.
- Published
- 2003
46. Mermin Ho vortices and monopoles in three-component spinor BEC
- Author
-
Xin Liu, Yi-Shi Duan, and Peng-ming Zhang
- Subjects
Condensed Matter::Quantum Gases ,Physics ,Annihilation ,Spinor ,Field (physics) ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Symmetry protected topological order ,Vortex ,Quantum mechanics ,Topological order ,Tensor ,Mathematical Physics ,Topological quantum number ,Mathematical physics - Abstract
In the light of the -mapping topological current theory, the Mermin–Ho vortices and the monopoles in three-component spinor BEC are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents which can be derived from the same field tensor kμν, and both these topological structures are characterized by the -mapping topological numbers—Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of Mermin–Ho vortices and the generation and annihilation of monopoles are also discussed.
- Published
- 2002
47. Decomposition theory of theU(1) gauge potential and the London assumption in topological quantum mechanics
- Author
-
Yi-Shi Duan, Xin Liu, and Peng-ming Zhang
- Subjects
Physics ,High Energy Physics::Lattice ,Rigorous proof ,Gauge (firearms) ,Expression (computer science) ,Condensed Matter Physics ,Topology ,Decomposition theory ,Quantum mechanics ,Decomposition (computer science) ,General Materials Science ,Gauge theory ,U-1 ,Topology (chemistry) ,Mathematical physics - Abstract
The decomposition theory of the U(1) gauge potential has been studied. A rigorous proof of the London assumption is given. By making use of this gauge potential decomposition and the -mapping topological current theory, the precise expression for × is obtained, and the topology in quantum mechanics is discussed.
- Published
- 2002
48. The configuration of a topological current and its physical structure: an application and paradigmatic evidence
- Author
-
Yi-Shi Duan, Shigang Chen, Li-Bin Fu, and Jie Liu
- Subjects
Physics ,Current (mathematics) ,Structure (category theory) ,FOS: Physical sciences ,General Physics and Astronomy ,Order (ring theory) ,Statistical and Nonlinear Physics ,Topology ,Physics - General Physics ,General Physics (physics.gen-ph) ,Physical structure ,Bifurcation theory ,Mathematical Physics ,Topology (chemistry) - Abstract
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between different structures happens at the bifurcation point of the topological current. In a self-interaction two-level system, the change of topological particles corresponds to change of energy levels., Comment: 9 pages, 2 figures
- Published
- 2002
49. [Untitled]
- Author
-
Hui Zhang, Yi-Shi Duan, and Guo-Hong Yang
- Subjects
Physics and Astronomy (miscellaneous) ,Field (physics) ,Quantitative Biology::Tissues and Organs ,General Mathematics ,Disclination ,Topology ,Condensed Matter::Soft Condensed Matter ,symbols.namesake ,Classical mechanics ,Bifurcation theory ,Liquid crystal ,Jacobian matrix and determinant ,Limit point ,Physics::Atomic and Molecular Clusters ,symbols ,Gravitational singularity ,Bifurcation ,Mathematics - Abstract
Using φ-mapping method and topological current theory, the properties and behaviors of disclination points in three-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination points, the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the general director field when the Jacobian determinant of the general director field does not vanish. When the Jacobian determinant vanishes, the origin, annihilation, and bifurcation of disclination points are detailed in the neighborhoods of the limit point and bifurcation point, respectively. The branch solutions at the limit point and the different directions of all branch curves at the first- and second-order degenerated points are calculated. It is pointed out that a disclination point with a higher strength is unstable and will evolve to the lower strength state through the bifurcation process. An original disclination point can split into at most four disclination points at one time.
- Published
- 2002
50. INNER STRUCTURE OF GAUSS–BONNET–CHERN THEOREM AND THE MORSE THEORY
- Author
-
Yi-Shi Duan and Peng-Ming Zhang
- Subjects
Mathematics - Differential Geometry ,Physics ,Nuclear and High Energy Physics ,Current (mathematics) ,Structure (category theory) ,FOS: Physical sciences ,General Physics and Astronomy ,Astronomy and Astrophysics ,Mathematical Physics (math-ph) ,High Energy Physics::Theory ,symbols.namesake ,Differential Geometry (math.DG) ,Gauss–Bonnet theorem ,Euler characteristic ,FOS: Mathematics ,symbols ,Mathematics::Differential Geometry ,Tensor ,General topology ,Mathematical Physics ,Morse theory ,Mathematical physics - Abstract
We define a new one form H^A based on the second fundamental tensor H^abA, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the phi-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the delta-function and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincare theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized., 10 pages
- Published
- 2001
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