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Search Results: 1 - 10 of 1213 matches for " exact invariant "
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Exact invariants and adiabatic invariants of the singular Lagrange system

Chen Xiang-Wei,Li Yan-Min,

中国物理 B , 2003,
Abstract: Based on the theory of symmetries and conserved quantities of the singular Lagrange system, the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations
陈向炜,刘翠梅,李彦敏
中国物理 B , 2006,
Abstract:
Characteristic Algebras of Fully Discrete Hyperbolic Type Equations
Ismagil T. Habibullin
Symmetry, Integrability and Geometry : Methods and Applications , 2005,
Abstract: The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS

Chen Xiang-wei,Shang Mei,Mei Feng-xiang,

中国物理 B , 2001,
Abstract: A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes-Cummings model
沈建其,朱红毅,符建
中国物理 B , 2002,
Abstract: On the basis of the fact that the two-level multiphoton Jaynes-Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.
Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
Luo Shao-Kai,Chen Xiang-Wei,Guo Yong-Xin,
罗绍凯
,陈向炜,郭永新

中国物理 B , 2007,
Abstract: Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
Exact invariants and adiabatic invariants of dynamical system of relative motion
Exact invariants and adiabatic invariantsof dynamical system of relative motion

Chen Xiang-Wei,Wang Xin-Min,Wang Ming-Quan,
陈向炜
,王新民,王明泉

中国物理 B , 2004,
Abstract: Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates
准坐标下完整系统的精确不变量与绝热不变量

Chen Xiang-Wei,Li Yan-Min,
陈向炜
,李彦敏

中国物理 B , 2005,
Abstract: Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of holonomic system are studied in terms of quasi-coordinates. The perturbation to symmetries for the holonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
Exact solutions of general time-dependent three-generator systems
一般三生成元含时系统的精确解

Zhu Hong-Yi,Shen Jian-Qi,
朱红毅
,沈建其

物理学报 , 2002,
Abstract: There exist a number of typical systems and models which possess the three generator Lie algebraic structure in quantum optics, atomic and molecular physics and condensed matter physics. The present paper obtains exact solutions of these time dependent three generator systems by making use of the Lewis Riesenfeld invariant theory and the invariant related unitary transformation formulation.
Surfaces of Revolution in the General Theory of Relativity  [PDF]
Taxiarchis Papakostas
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.614206
Abstract: We present a class of axially symmetric and stationary spaces foliated by a congruence of surfaces of revolution. The class of solutions considered is that of Carter’s family [A] of spaces and we try to find a solution to Einstein’s equations in the presence of a perfect fluid with heat flux. This approach is an attempt to find an interior solution that could be matched to a corresponding exterior solution across a surface of zero hydrostatic pressure. The presence of a congruence of surfaces of revolution, described as the quotient space of the commoving observers, can be useful to the determination of the surface of zero pressure. Finally we present two formal solutions representing ellipsoids of revolutions.
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