共查询到20条相似文献,搜索用时 31 毫秒
1.
REN Ji-Rong LI Ran DUAN Yi-Shi 《理论物理通讯》2008,50(7):53-58
We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the Ф-mapping topological current theory. The main purpose of this paper is to present a new theoretical framework, which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space R^2n-1. For the sake of this purpose we introduce a topological tensor current, which can naturally deduce the (n- 1)-dimensional topological defect in R^2n-1 space. If these (n- 1)-dimensional topological defects are closed oriented submanifolds of R^2n-1, they are just the (n - 1)-dimensional knots. The linking number of these knots is well defined. Using the inner structure of the topological tensor current, the relationship between Hopf invariant and the linking numbers of the higher-dimensional knots can be constructed. 相似文献
2.
Based on the concept of adiabatic invariant, the perturbation to Lie-Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie-Mei symmetry for the system is presented, and the criterion of the perturbation to Lie-Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained. 相似文献
3.
A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems
Considering full perturbation to infinitesimal generators in the Mei structure equation, a new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported. 相似文献
4.
We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott (HPS) form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary (thus maximally T-violating) and to have a strength in energy scale no greater (but perhaps smaller) than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)^2) ≈ 3.5 ×10^-3 from their HPS values. Assuming that (mμ/mτ)^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters. 相似文献
5.
ZHANG Ming-Jiang FANG Jian-Hui LU Kai 《理论物理通讯》2008,50(8):326-330
Based on the concept of adiabatic invariant, the perturbation to Noether-Lie symmetry and adiabatic invariants for mechanical systems in phase space are studied. The criterion of the Noether Lie symmetry for the perturbed system is given, and the definition of the perturbation to Noether-Lie symmetry for the system under the action of small disturbance is presented. Meanwhile, the Noether adiabatic invariants and the generalized Hojman adiabatic invariants of the perturbed system are obtained. 相似文献
6.
In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z(x, t). [t is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology. 相似文献
7.
It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants. This extends the result to the two-component Ermakov system. 相似文献
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9.
将Ermakov系统加以推广,得出受到与速度平方成正比的力的变频率谐振子的不变量,求出其普遍解. 相似文献
10.
Normal coordinate in harmonic crystal obtained virtue of the classical correspondence of the invariant eigen-operator 下载免费PDF全文
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Left. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method. 相似文献
11.
WU Hao FAN Hong-Yi 《理论物理通讯》2008,50(12):1348-1350
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise. 相似文献
12.
By means of the classical symmetry method, we investigate two types of the (2+1)-dimensional nonlinear Klein-Gorden equation. For the wave equation, we give out its symmetry group analysis in detail. For the second type of the (2+1)-dimensional nonlinear Klein-Gorden equation, an optimal system of its one-dimensional subalgebras is constructed and some corresponding two-dimensional symmetry reductions are obtained. 相似文献
13.
Classification and reduction of the generalized fourth-order nonlinear differential equations arising from the liquid films are considered. It is shown that these equations have solutions on subspaces of the polynomial, exponential or trigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n = 4,..., 9. Several examples of exact solutions are presented. 相似文献
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15.
The original formula to calculate the tunneling rate through event horizons is apparently dependent on the type of coordinates used.In this paper,we propose an invariant expression under canonical transformations to study the tunneling effect.Moreover,the problem of factor 2 is solved naturally.As an application of this expression,we obtain the same tunneling rate both in the Schwarzschild and the Painleve′coordinates.It is shown that once the suitable formula to calculate tunneling rate is correctly identified,the tunneling method is manifestly covariant. 相似文献
16.
ZHANG Xue ZHENG Tai-Yu ZHENG Li 《理论物理通讯》2008,50(10):955-960
The system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one. 相似文献
17.
WANG Yong ZHANG Shun-Li 《理论物理通讯》2008,49(1):17-21
This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry (A GCS). Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate invariant solutions to the resulting equations can also be obtained. 相似文献
18.
We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is timedependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically. 相似文献
19.
By Lie symmetry method, the Lie point symmetries and its Kac Moody-Virasoro (KMV) symmetry algebra of (2+1)-dimensional dispersive long-wave equation (DLWE) are obtained, and the finite transformation of DLWE is given by symmetry group direct method, which can recover Lie point symmetries. Then KMV symmetry algebra of DLWE with arbitrary order invariant is also obtained. On basis of this algebra the group invariant solutions and similarity reductions are also derived. 相似文献
20.
In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces(“centrifugal potential”) in addition to linear forces (“harmonical potential”) are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied. 相似文献