Doubly Exotic Nth-Order Superintegrable Classical Systems Separating in Cartesian Coordinates
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Mathematical physics on superintegrable classical systems with exotic potentials; a theory result, not a study of research.
The work develops mathematical results for superintegrable systems rather than studying research.
Mathematical physics of superintegrable classical systems, not metaresearch.
Résumé
Superintegrable classical Hamiltonian systems in two-dimensional Euclidean space E 2 are explored. The study is restricted to Hamiltonians allowing separation of variables V (x, y) = V 1 (x) + V 2 (y) in Cartesian coordinates. In particular, the Hamiltonian H admits a polynomial integral of order N > 2. Only doubly exotic potentials are considered. These are potentials where none of their separated parts obey any linear ordinary differential equation. An improved procedure to calculate these higher-order superintegrable systems is described in detail. The two basic building blocks of the formalism are non-linear compatibility conditions and the algebra of the integrals of motion. The case N = 5, where doubly exotic confining potentials appear for the first time, is completely solved to illustrate the present approach. The general case N > 2 and a formulation of inverse problem in superintegrability are briefly discussed as well.
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La notice
- Revue
- Symmetry Integrability and Geometry Methods and Applications
- Thématique
- Quantum Mechanics and Non-Hermitian Physics
- Domaine
- Physics and Astronomy
- Établissements canadiens
- —
- Organismes subventionnaires
- Université de MontréalCentre de Recherches Mathématiques
- Mots-clés
- Cartesian coordinate systemOrder (exchange)Bipolar coordinatesSuperintegrable Hamiltonian systemOrthogonal coordinatesMathematicsIntegrable systemPhysicsMathematical physicsPure mathematicsMathematical analysisGeometryHamiltonian system
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- oui