Navegando por Autor "Zhang, P. M."
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Item Conformal Killing tensors and covariant Hamiltonian dynamics.(2014) Cariglia, Marco; Gibbons, G. W.; Holten, J. W. van; Horvathy, P. A.; Zhang, P. M.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 H´enon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.Item Ion traps and the memory effect for periodic gravitational waves.(2018) Zhang, P. M.; Cariglia, Marco; Duval, C.; Elbistan, M.; Gibbons, G. W.; Horvathy, P. A.The Eisenhart lift of a Paul trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelt’s Penning trap is, in turn, related to circularly polarized periodic gravitational waves, sought in inflationary models. Similar equations also govern the Lagrange points in celestial mechanics. The explanation is provided by anisotropic oscillators.