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Integrable potentials on spaces with curvature from quantum groups | | Angel Ballesteros
; Francisco J. Herranz
; Orlando Ragnisco
; | | Date: |
30 May 2005 | | Journal: | J. Phys. A: Math. Gen. 38 (2005) 7129-7144 | | Subject: | Mathematical Physics; Quantum Algebra; Exactly Solvable and Integrable Systems | math-ph math.MP math.QA nlin.SI | | Abstract: | A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson coalgebra. All these spaces have a non-constant curvature that depends on the deformation parameter z. As particular cases, the analogues of the harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed. Another deformed Hamiltonian is also shown to provide superintegrable systems on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant curvature that exactly coincides with z. According to each specific space, the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers. The non-deformed limit z=0 of all these Hamiltonians can then be regarded as the zero-curvature limit (contraction) which leads to the corresponding (super)integrable systems on the flat Euclidean and Minkowskian spaces. | | Source: | arXiv, math-ph/0505081 | | Services: | Forum | Review | PDF | Favorites | |
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