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1.
WANG Ji-Biao REN Ji-Rong LI Ran 《理论物理通讯》2009,51(2):335-340
Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas 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 topological term n^→·(Эin^→×Эjn^→), and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons. 相似文献
2.
Shu-Fan Mo Ji-Rong Ren Li Zhao Tao Zhu 《International Journal of Theoretical Physics》2009,48(3):645-657
In this paper, by making use of Duan’s topological current theory, the branch process of Chern-Simons (CS) p-branes is discussed in detail. Chern-Simons (CS) p-branes are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation
points and higher degenerated points systematically of the vector order parameter field
. Furthermore, it is also shown that CS p-branes are found splitting or merging at the degenerate point of field function
but the total topological charges of the CS p-branes are still unchanged. 相似文献
3.
4.
In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B.
PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq 相似文献
5.
We examine the contribution of electromagnetic field to the atomic spin, by adopting two different, both gauge invariant definitions of the electromagnetic angular momentum: \vec{J}I ≡ ∫d3 x ε0 \vec{r} X (\vec{E} X \vec{B}) and \vec{J}II ≡ ∫d3 x ( ε0 \vec{E} X \vec{A}^\bot + ε0 Ei \vec{r} X \vec{\nabla }A^{\bot}i ). Notably, at the classical level, \vec{J}II gives an exactly null result while \vec{J}I gives a finite value. This suggests that \vec{J}II leads to a simpler and more reasonable picture of the atomic spin, therefore qualifies as a more appropriate definition of the electromagnetic angular momentum. Our observation gives important hint on the delicate issue of gluon contribution to the nucleon spin. 相似文献
6.
Quintessence field is a widely-studied candidate of dark energy. There is ``tracker solution' in quintessence models, in which evolution of the field ø at present times is not sensitive to its initial conditions. When the energy density of dark energy is neglectable (Ωø<< 1), evolution of the tracker solutioncan be well analysed from ``tracker equation'. In this paper, we try tostudy evolution of the quintessence field from ``full tracker equation',which is valid for all spans of Ωø. We get stable fixed points of wø and Ωø (noted as \hat{w}ø and \hat{Ω}ø) from the ``full tracker equation', i.e., wø and Ωø will always approach \hat{w}ø and \hat{Ω}ø respectively. Since \hat{w}ø and \hat{Ω}ø are analytic functions of ø, analytic relation of \hat{w}ø ~ \hat{Ω}ø can be obtained, which is a good approximation for the wø ~ Ωø relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities \hat{w}ø < wø and \hat{Ω}ø < Ωø are statisfied if the wø (or \hat{w}ø) decreases with time. In this way, the potential U(ø) can be constrained directly from observations, by no need of solving the equations of motion numerically. 相似文献
7.
By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(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 χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes. 相似文献
8.
Using SU(2) gauge field theory and the-mapping method, we quantize the magnetic monopolesat the topological level and determine their quantumnumbers by the Hopf indices and Brouwer degrees of the -mapping. Then, based on the implicitfunction theorem and Taylor expansion, we study theorigin and bifurcation theories of magnetic monopoles atthe limit points and bifurcation points (includingfirst-order and second-order degenerate points),respectively. We point out that a magnetic monopole cansplit into at most four particles at one time. 相似文献
9.
A self-consistentU(1)-gauge model in gravitational field is investigated. The exact solutions of two types of corresponding field equations are obtained. These solutions can be interpreted as magnetic monopoles. The first solution is regular forr 0 and provides an everywhere regular geometry, the second one has a physical singularity. In order to guarantee the stability of the monopoles we introduce the notion of a gravitational topological charge using de Rham's cohomology theory. This topological charge describes the sizes and the inner structure of the monopole. 相似文献
10.
We investigate the topological properties of a trimerized parity–time(PT)symmetric non-Hermitian rhombic lattice.Although the system is PT-symmetric,the topology is not inherited from the Hermitian lattice;in contrast,the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices.The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology.Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach.In addition,the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice.Our findings reveal the topological properties of the??PT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases. 相似文献
11.
Miguel Ballesteros Jérémy Faupin Jürg Fröhlich Baptiste Schubnel 《Communications in Mathematical Physics》2015,337(2):633-680
A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass m, finitely many excited states and an electric dipole moment, \({\vec{d}_0 = -\lambda_{0} \vec{d}}\), where \({\| d^{i}\| = 1, i = 1, 2, 3,}\) and \({\lambda_0}\) is proportional to the elementary electric charge. The interaction of the atom with the radiation field is described with the help of the Ritz Hamiltonian, \({-\vec{d}_0 \cdot \vec{E}}\), where \({\vec{E}}\) is the electric field, cut off at large frequencies. A mathematical study of the Lamb shift, the decay channels and the life times of the excited states of the atom is presented. It is rigorously proven that these quantities are analytic functions of the momentum \({\vec{p}}\) of the atom and of the coupling constant \({\lambda_0}\), provided \({\vert\vec{p} \vert < mc}\) and \({\vert \Im \vec{p} \vert}\) and \({\vert \lambda_{0} \vert}\) are sufficiently small. The proof relies on a somewhat novel inductive construction involving a sequence of ‘smooth Feshbach–Schur maps’ applied to a complex dilatation of the original Hamiltonian, which yields an algorithm for the calculation of resonance energies that converges super-exponentially fast. 相似文献
12.
REN Ji-Rong XU Dong-Hui ZHANG Xin-Hui LI Ran 《理论物理通讯》2007,47(5):944-948
In this paper, using the Φ-mapping theory, it is shown that two kinds of topological defects, i.e., the vortex lines and the monopoles exist in the helical configuration of magnetic field in triplet superconductors. And the inner topological structure of these defects is studied. Because the knot solitons in the triplet superconductors are characterized by the Hopf invariant, we also establish a relationship between the Hopf invariant and the linking number of knots family, and reveal the inner topological structure of the Hopf invariant. 相似文献
13.
We study the question of magnetic confinement of quantum particles on the unit disk \({\mathbb {D}}\) in \({\mathbb {R}^2}\) , i.e. we wish to achieve confinement solely by means of the growth of the magnetic field \({B(\vec x)}\) near the boundary of the disk. In the spinless case, we show that \({B(\vec x)\ge \frac{\sqrt 3}{2}\cdot\frac{1}{(1-r)^2}-\frac{1}{\sqrt 3}\frac{1}{(1-r)^2\ln \frac{1}{1-r}}}\) , for \({|\vec x|}\) close to 1, insures the confinement provided we assume that the non-radially symmetric part of the magnetic field is not very singular near the boundary. Both constants \({\frac{\sqrt 3}{2}}\) and \({-\frac{1}{\sqrt 3}}\) are optimal. This answers, in this context, an open question from Colin de Verdière and Truc (Ann Inst Fourier 2011, Preprint, arXiv:0903.0803v3). We also derive growth conditions for radially symmetric magnetic fields which lead to confinement of spin 1/2 particles. 相似文献
14.
Ashok Kumar 《Applied physics. B, Lasers and optics》2013,110(1):117-121
Terahertz radiation generation by second-order nonlinear mixing of laser $ (\omega_{1} ,\,\vec{k}_{1} ) $ and its frequency shifted second harmonic $ \omega_{2} = 2\omega_{1} - \omega ,\,\,\vec{k}_{2} \, $ $ (\omega \ll \omega_{1} ) $ in a plasma, in the presence of an obliquely inclined density ripple of wave number $ \vec{q} $ , are investigated. The lasers exert ponderomotive force on electrons and drive density perturbations at $ (2\omega_{1} ,\,2\vec{k}_{1} - \vec{q}) $ and $ (\omega_{1} - \omega_{2} ,\,\vec{k}_{1} - \vec{k}_{2} - \vec{q}) $ . These perturbations beat with the electron oscillatory velocities due to the lasers to produce a nonlinear current at $ \omega ,\,\vec{k} = 2\vec{k}_{1} - \vec{k}_{2} - \vec{q} $ , resonantly driving the terahertz radiation when $ \vec{q} $ satisfies the phase matching condition. The radiated THz intensity depends on the relative polarization of the lasers and scales as the square of intensity of the fundamental laser and linearly with the square root of the intensity of the second harmonic. The THz emission is maximized when the polarization of the lasers is aligned. These results are consistent with the recent experimental results. 相似文献
15.
We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G 3 = O(3) ? P 3. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: \(\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}\), where I j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: \(I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)\). 相似文献
16.
A. Ojeda González A. Prestes A. Nilson Laurindo Sousa 《Brazilian Journal of Physics》2016,46(4):408-414
We discuss the relationship between the Coulomb gauge, the existence of an invariant axis, and the dimensionality (2-D or 2\(\frac {1}{2}\)-D) of the magnetic field in a mathematical-physical formalism that leads us to the Grad-Shafranov (GS) equation. In the literature, we found that a 2-D magnetic structure is used as a prerequisite to derive the GS equation from the Vlasov equation. However, other consulted works are based on a 2\(\frac {1}{2}\)-D (two-and-a-half) magnetic structure as a prerequisite to derive the GS equation from the balance of forces between the pressure gradient and the magnetic force, respectively. We replaced the magnetic vector potential on Ampère’s equation and used the Coulomb gauge to obtain a system of three Poisson equations, one for each component. We also used the same procedure explained above, but without the Coulomb gauge. Comparing z-component in both equation systems, we concluded that there are two possible solutions. We suggest using a 2\(\frac {1}{2}\)-D magnetic field configuration instead of a 2-D, when working with kinetic theory or magnetostatic equilibrium to derive the GS equation. We clarified that there is no relationship between the Coulomb gauge and the magnetic field dimensionality. In this problem, the invariant axis condition is imposed, which means that \(\vec {\nabla }\cdot \vec {A}\) is independent of z, i.e., \(\vec {\nabla }\cdot \vec {A}\) could have any value in which an invariant axis is a sufficient condition to obtain the GS equation. 相似文献
17.
D. V. Petrov M. P. Petrov B. Hilling M. Lemmer M. Imlau 《Applied physics. B, Lasers and optics》2009,95(3):483-488
An impressive linear influence of a magnetic field on optically generated trap-recharging waves (TRW) has been observed in
InP:Fe and GaAs:Cr. The phenomenon appears for the particular orientation of
parallel to the samples’ surface and orthogonal to the direction of the electric field
and wave vector of the TRW
. The results are qualitatively explained taking into account the Lorentz force and a pronounced inhomogeneity of the charge
transport and of the TRW parameters. 相似文献
18.
DUAN Yi-Shi ZHAO Li ZHANG Xin-Hui SI Tie-Yan 《理论物理通讯》2007,47(6):1125-1128
A topological theory of liquid crystal films in the presence of defects is developed based on the Ф-mapping topological current theory. By generalizing the free-energy density in "one-constant" approximation, a covariant free- energy density is obtained, from which the U(1) gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of Ф-mapping. 相似文献
19.
A. Yu. Gufan O. V. Kukin Yu. M. Gufan I. A. Osipenko 《Bulletin of the Russian Academy of Sciences: Physics》2012,76(3):328-338
The third-order elastic modulus of α-Fe were calculated based on the computation of lattice sums. The lattice sums were determined
using an integer rational basis of invariants composed by vectors connecting equilibrium atomic positions in the crystal lattice.
Irreducible interactions within clusters consisting of atomic pairs and triplets were taken into account in performing the
calculations. Comparison with experimental data showed that the potential can be written in the form of e9 = - ?i,k A19 rik - 6 + ?i,k A29 rik - 12 + ?i,k,l Q9 I9 - 1\varepsilon _9 = - \sum\nolimits_{i,k} {A_{19} r_{ik}^{ - 6} } + \sum\nolimits_{i,k} {A_{29} r_{ik}^{ - 12} + \sum\nolimits_{i,k,l} {Q_9 I_9^{ - 1} } }, where I9 = [(r)\vec]ik2 [ ( [(r)\vec]ik [(r)\vec]kl )2 + ( [(r)\vec]li [(r)\vec]ik )2 ] + [(r)\vec]kl2 [ ( [(r)\vec]ik [(r)\vec]kl )2 + ( [(r)\vec]kl [(r)\vec]li )2 ] + [(r)\vec]li2 [ ( [(r)\vec]li [(r)\vec]ik )2 + ( [(r)\vec]kl [(r)\vec]li )2 ]I_9 = \vec r_{ik}^2 \left[ {\left( {\vec r_{ik} \vec r_{kl} } \right)^2 + \left( {\vec r_{li} \vec r_{ik} } \right)^2 } \right] + \vec r_{kl}^2 \left[ {\left( {\vec r_{ik} \vec r_{kl} } \right)^2 + \left( {\vec r_{kl} \vec r_{li} } \right)^2 } \right] + \vec r_{li}^2 \left[ {\left( {\vec r_{li} \vec r_{ik} } \right)^2 + \left( {\vec r_{kl} \vec r_{li} } \right)^2 } \right]. If the values of [(r)\vec]ik\vec r_{ik} are scaled in half-lattice constant units, then A19 = 1.22
ë t9
û GPa, A29 = 5.07 ×102
ë t15
û GPa, Q9 = 5.31
ë t9
û GPaA_{19} = 1.22\left\lfloor {\tau ^9 } \right\rfloor GPa, A_{29} = 5.07 \times 10^2 \left\lfloor {\tau ^{15} } \right\rfloor GPa, Q_9 = 5.31\left\lfloor {\tau ^9 } \right\rfloor GPa, and τ = 1.26 ?. It is shown that the condition of thermodynamic stability of a crystal requires that we allow for irreducible
interactions in atom triplets in at least four coordination spheres. The analytical expressions for the lattice sums determining
the contributions from irreducible interactions in the atom triplets to the second- and third-order elastic moduli of cubic
crystals in the case of interactions determined by I
9 are presented in the appendix. 相似文献
20.
Using the bosonic coherent state representation and the Schwinger bosonic operator realization of angular momentum we find the formula for the quantum Hamiltonian H =iaiUijUjl a1 for SU(2) rotation U, in this way we further specify the angular velocity w, iUU = (1/2)σ·ω, where σ is the Pauli matrix. Though the spin as a quantum observable has no classical correspondence, we may still mimic it as a rigid body rotation characterized by 3 Euler angles, and calculate its Pseudo-classical rotational partition function of spin one-half. 相似文献