scholarly journals Weyl’s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics

2007 ◽  
Vol 48 (5) ◽  
pp. 052107 ◽  
Author(s):  
M. I. Krivoruchenko ◽  
Amand Faessler
Keyword(s):  
Canonical Coordinates ◽  
Heisenberg Operators

scholarly journals Forecasting Hamiltonian dynamics without canonical coordinates

2021 ◽  
Author(s):  
Anshul Choudhary ◽  
John F. Lindner ◽  
Elliott G. Holliday ◽  
Scott T. Miller ◽  
Sudeshna Sinha ◽  
...  
Keyword(s):  
Hamiltonian Dynamics ◽  
Canonical Coordinates

scholarly journals Construction of canonical coordinates for exponential Lie groups

2009 ◽  
Vol 361 (12) ◽  
pp. 6283-6348 ◽  
Author(s):  
Didier Arnal ◽  
Bradley Currey ◽  
Bechir Dali
Keyword(s):  
Lie Groups ◽  
Canonical Coordinates ◽  
Exponential Lie Groups

scholarly journals Smale spaces via inverse limits

2013 ◽  
Vol 34 (6) ◽  
pp. 2066-2092 ◽  
Author(s):  
SUSANA WIELER
Keyword(s):  
Dynamical System ◽  
Inverse Limits ◽  
Canonical Coordinates ◽  
Chaotic Dynamical System ◽  
Smale Space ◽  
Smale Spaces ◽  
Special Case ◽  
Basic Sets

AbstractA Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom $A$ systems are a key class of examples. We consider the special case of irreducible Smale spaces with zero-dimensional contracting directions, and characterize these as stationary inverse limits satisfying certain conditions.

Symplectic calculation of the outboard magnetic footprint from noise and error fields in the DIII-D

2011 ◽  
Vol 77 (6) ◽  
pp. 785-802
Author(s):  
HALIMA ALI ◽  
ALKESH PUNJABI ◽  
ERNEST NYAKU
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Generating Function ◽  
Magnetic Field Line ◽  
Physical Space ◽  
Physical Parameters ◽  
Canonical Coordinates ◽  
Step Size ◽  
Magnetic Perturbation ◽  
Collector Plate

AbstractThe backward symplectic DIII-D map and continuous symplectic analog of the map for magnetic field line trajectories in the DIII-D [10] (Luxon, J. L. and Davis, L. E. 1985 Fusion Technol.8, 441) in natural canonical coordinates are used to calculate the magnetic footprint on the outboard collector plate of the DIII-D tokamak from the field errors and internal topological noise. The equilibrium generating function for the DIII-D used in the map very accurately represents the magnetic geometry of the DIII-D. The step-size of the map is kept considerably small so that the magnetic perturbation added from symplectic discretization of the Hamiltonian equations of the magnetic field line trajectories is very small. The natural canonical coordinates allow inverting to the real physical space. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size then together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The footprint is in the form of toroidally winding helical strips. The area of footprint scales as 1st power of amplitude. The physical parameters as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near X-point for lines that strike and that do not strike differs by about four orders of magnitude. The flux loss decreases for high values of amplitude of perturbation.

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