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Cariglia, M; Gibbons, GW; van Holten, JW; Horvathy, PA; Zhang, PM; Cariglia, M (reprint author), Univ Fed Ouro Preto, DEFIS, Campus Morro Cruzeiro, BR-35400000 Ouro Preto, MG, Brazil.
Conformal killing tensors and covariant Hamiltonian dynamics
Source PublicationJOURNAL OF MATHEMATICAL PHYSICS
Language英语
KeywordPerturbed Hydrogen-atom Der-waals Interaction Henon-heiles System Variable-separation Painleve Property Jacobi Equation Quantum Dots Symmetry Integrals Motion
AbstractA covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Henon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six. (C) 2014 AIP Publishing LLC.
2014
ISSN0022-2488
Volume55Issue:12Pages:122702
Subject AreaPhysics
DOI10.1063/1.4902933
Indexed BySCI
Funding OrganizationNational Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06] ; National Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06] ; National Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06] ; National Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06]
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Cited Times:14[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/15555
Collection理论物理所科研产出_SCI论文
Corresponding AuthorCariglia, M (reprint author), Univ Fed Ouro Preto, DEFIS, Campus Morro Cruzeiro, BR-35400000 Ouro Preto, MG, Brazil.
Recommended Citation
GB/T 7714
Cariglia, M,Gibbons, GW,van Holten, JW,et al. Conformal killing tensors and covariant Hamiltonian dynamics[J]. JOURNAL OF MATHEMATICAL PHYSICS,2014,55(12):122702.
APA Cariglia, M,Gibbons, GW,van Holten, JW,Horvathy, PA,Zhang, PM,&Cariglia, M .(2014).Conformal killing tensors and covariant Hamiltonian dynamics.JOURNAL OF MATHEMATICAL PHYSICS,55(12),122702.
MLA Cariglia, M,et al."Conformal killing tensors and covariant Hamiltonian dynamics".JOURNAL OF MATHEMATICAL PHYSICS 55.12(2014):122702.
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