3d Symplectic Map
نویسنده
چکیده
Quantum 3D R – matrix in the classical (i. e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem for it is a system of linear equations playing the role of the monodromy matrix in 2D models. A generating function for the integrals of motion is constructed as a determinant of the auxiliary system. PACS: 05.50; 02.10; 02.20
منابع مشابه
A Differential Algebraic Integration Algorithm for Symplectic Mappings in Systems with Three-Dimensional Magnetic Field
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3D magnetic field are then obtained through slice-by-slice sympl...
متن کاملOn Contact and Symplectic Lie Algeroids
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...
متن کاملExtraction of Lie Map from Realistic 3d Magnetic Field Data*
We present a method to extract the Lie map from the realistic magnetic field data of arbitrary magnet. The multi-particle tracking results are fitted into Taylor maps, which can be factorized into a Lie map by using DragtFinn's method [1]. This method is validated by comparing against the COSY-infinity code [2] for a soft-edge quadrupole model. Examples of extracting the symplectic maps for the...
متن کاملFast Intra Mode Decision for Depth Map coding in 3D-HEVC Standard
three dimensional- high efficiency video coding (3D-HEVC) is the expanded version of the latest video compression standard, namely high efficiency video coding (HEVC), which is used to compress 3D videos. 3D videos include texture video and depth map. Since the statistical characteristics of depth maps are different from those of texture videos, new tools have been added to the HEVC standard fo...
متن کاملRenormalization Group Reduction of Symplectic Maps
By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a ...
متن کامل