scholarly journals TOPOLOGICAL ASPECT OF BLACK HOLE WITH SKYRME HAIR

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5895-5903 ◽  
Author(s):  
YISHI DUAN ◽  
XINHUI ZHANG ◽  
LI ZHAO
Keyword(s):  
Black Hole ◽  
Current Theory ◽  
Topological Aspect ◽  
Baryon Charge ◽  
Topological Current

Based on the ϕ-mapping topological current theory, we show that the presence of the black hole leaves fractional baryon charge outside the horizon in the Einstein–Skyrme theory. A topological current is derived from the Einstein–Skyrme system, which corresponds to the monopoles around the black hole. The branch process (splitting, merging and intersection) is simply discussed during the evolution of the monopoles.

TOPOLOGICAL SOLUTION OF BOHMIAN QUANTUM MECHANICS

2009 ◽  
Vol 24 (06) ◽  
pp. 453-461 ◽  
Author(s):  
XUGUANG SHI ◽  
MING YU ◽  
YISHI DUAN
Keyword(s):  
Quantum Mechanics ◽  
Particle System ◽  
World Line ◽  
Zero Point ◽  
Current Theory ◽  
Brouwer Degree ◽  
Topological Current ◽  
The World ◽  
Bohmian Quantum Mechanics ◽  
De Broglie Bohm

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.

Skyrmion Excitations in Graphene

2014 ◽  
Vol 887-888 ◽  
pp. 960-965 ◽  
Author(s):  
Bu Da Zhao ◽  
Ming Xiang
Keyword(s):  
Potential Theory ◽  
Limit Point ◽  
Bifurcation Theory ◽  
Current Theory ◽  
Gauge Potential ◽  
Topological Current ◽  
Mapping Theory

By making use of theφ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of (2+1)-dimensional graphene. It is shown that the topological numbers are Hopf indices and Brower degrees. Based on the bifurcation theory of theφ-mapping theory, it is founded that the skyrmions can be generated or annihilated at the limit point (the generation and annihilation of skyrmion-antiskyrmion pairs).

REDUCED QUANTUM TOPOLOGICAL TRAJECTORY IN COHERENCE AND DECOHERENCE

2011 ◽  
Vol 26 (18) ◽  
pp. 1363-1373 ◽  
Author(s):  
XUGUANG SHI ◽  
YISHI DUAN
Keyword(s):  
Density Matrix ◽  
Matrix Theory ◽  
Current Theory ◽  
Topological Invariant ◽  
Reduced Density Matrix ◽  
Quantum Trajectory ◽  
Winding Number ◽  
Topological Current ◽  
Reduced Density ◽  
Density Matrix Theory

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.

GEOMETRIC DUALITY AND CHERN–SIMONS MODIFIED GRAVITY

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1323-1327 ◽  
Author(s):  
L. A. CABRAL
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Modified Gravity ◽  
Kerr Metric ◽  
Nontrivial Solutions ◽  
Topological Current ◽  
Chern Simons ◽  
Hilbert Action ◽  
Black Hole Solutions ◽  
Geometric Duality

We consider a theory which involves an extension of general relativity known as Chern–Simons modified gravity (CSMG). In this theory the standard Einstein–Hilbert action is extended with a gravitational Pontryagin density that is obtained from a divergence of a Chern–Simons topological current. The extended theory has the standard Schwarzchild metric as solution, however, only a perturbed Kerr metric holds solution. From the exact Kerr metric we construct dual metrics to search for rotating black hole solutions. The conditions on the Killing tensors associated with dual metrics entail nontrivial solutions to CSMG.

0 + 1-DIMENSIONAL TQFT: FROM HILBERT VECTOR SPACE TO TANGLE CATEGORY

2013 ◽  
Vol 10 (03) ◽  
pp. 1250087
Author(s):  
XU-GUANG SHI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Space ◽  
Current Theory ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Topological Quantum ◽  
Topological Current ◽  
Zero Points

In general, topological quantum field theory (TQFT) is studied in detail from the n-dimensional cobordism (nCob) to the Hilbert vector space. However, we study the TQFT in the different way in this paper, that is, the TQFT is studied from the Hilbert vector space to nCob. To do this, the theory called the ϕ-mapping topological current theory is used. The relation between the objects and zero points of the Hilbert states in the Hilbert vector space is studied in this frame. The relation between the morphism and topological current is revealed too.

TOPOLOGICAL ASPECTS OF THE PROTON VORTEX CLUSTERS IN THE CORE OF A NEUTRON STAR

2009 ◽  
Vol 18 (12) ◽  
pp. 1839-1849
Author(s):  
JUN LIANG ◽  
YISHI DUAN
Keyword(s):  
Neutron Star ◽  
Topological Structure ◽  
Order Parameter ◽  
Current Theory ◽  
Bifurcation Points ◽  
The Core ◽  
Topological Current ◽  
London Equation ◽  
Zero Points ◽  
Topological Charges

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.

SKYRMION EXCITATIONS OF SPIN HALL EFFECT IN ATOMS

2009 ◽  
Vol 23 (16) ◽  
pp. 1975-1982 ◽  
Author(s):  
JI-BIAO WANG ◽  
JI-RONG REN
Keyword(s):  
Hall Effect ◽  
Bifurcation Point ◽  
Bifurcation Theory ◽  
Atomic System ◽  
Current Theory ◽  
Spin Hall Effect ◽  
Gauge Potential ◽  
Optical Fields ◽  
Topological Current ◽  
Mapping Theory

By making use of ϕ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of spin Hall effect induced by optical fields in neutral atomic system. It is shown that the topological structures of these skyrmions are characterized by ϕ-mapping topological numbers: Hopf indices and Brouwer degrees. Based on the bifurcation theory of ϕ-mapping theory, it is found that the skyrmions can be generated or annihilated at the limit point and they encounter, split or merge at the bifurcation point.

TOPOLOGICAL OBJECTS IN THE O(3) NONLINEAR SIGMA MODEL

2007 ◽  
Vol 22 (31) ◽  
pp. 2379-2386
Author(s):  
PENG-MING ZHANG ◽  
XI-GUO LEE ◽  
SHAO-FENG WU ◽  
YI-SHI DUAN
Keyword(s):  
Sigma Model ◽  
Topological Defects ◽  
Current Theory ◽  
Gauge Potential ◽  
Nonlinear Sigma Model ◽  
Dimensional Model ◽  
Vortex Lines ◽  
Dimensional Spacetime ◽  
Topological Current ◽  
Topological Charges

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.

TOPOLOGICAL STRUCTURE OF VORTEX LINES OF QUANTUM ELECTRON PLASMAS IN THREE-DIMENSIONAL SPACE

2009 ◽  
Vol 23 (11) ◽  
pp. 2439-2447
Author(s):  
XUGUANG SHI ◽  
YISHI DUAN
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Current Theory ◽  
Brouwer Degree ◽  
Electron Plasmas ◽  
The Core ◽  
Vortex Lines ◽  
Quantum Electron ◽  
Topological Current ◽  
Three Dimensional Space

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.

scholarly journals A NEW DESCRIPTION OF COSMIC STRINGS IN BRANE WORLD SCENARIO

2008 ◽  
Vol 23 (24) ◽  
pp. 2023-2030
Author(s):  
YI-SHI DUAN ◽  
LI-DA ZHANG ◽  
YU-XIAO LIU
Keyword(s):  
Magnetic Flux ◽  
Cosmic String ◽  
Cosmic Strings ◽  
Current Theory ◽  
Brane World ◽  
Higgs Model ◽  
Gauge Potential ◽  
Topological Description ◽  
Topological Current ◽  
Effective Description

In the light of ϕ-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.

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