Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
arXiv:math-ph/0307013 · doi:10.1088/0305-4470/36/42/007
Abstract
A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.
19 Latex pages, No figures
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- Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
- Integrable perturbations of the N-dimensional isotropic oscillator
- An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
- Quantum group deformation of the Kittel--Shore model