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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 | |
发表期刊 | JOURNAL OF MATHEMATICAL PHYSICS |
语种 | 英语 |
关键词 | Perturbed Hydrogen-atom Der-waals Interaction Henon-heiles System Variable-separation Painleve Property Jacobi Equation Quantum Dots Symmetry Integrals Motion |
摘要 | A 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 | |
ISSN | 0022-2488 |
卷号 | 55期号:12页码:122702 |
学科领域 | Physics |
DOI | 10.1063/1.4902933 |
收录类别 | SCI |
项目资助者 | 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] ; National Natural Science Foundation of China [11035006, 11175215]; Chinese Academy of Sciences [2010TIJ06] |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.itp.ac.cn/handle/311006/15555 |
专题 | SCI期刊论文 |
通讯作者 | Cariglia, M (reprint author), Univ Fed Ouro Preto, DEFIS, Campus Morro Cruzeiro, BR-35400000 Ouro Preto, MG, Brazil. |
推荐引用方式 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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文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 | ||
Conformal killing te(805KB) | 开放获取 | CC BY-NC-SA | 请求全文 |
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