Cuboctahedric Higgs oscillator from the Calogero model

Abstract

We exclude the center of mass of the N-particle rational Calogero model and consider the angular part of the resulting Hamiltonian. We show that it describes the motion of the particle on (N-2)-dimensional sphere interacting with N(N-1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers define the vertexes of an Archimedean solid called cuboctahedron.

8 pages, 2 figures, revised version accepted in J. Phys. A, new material on superintegrability and refs added

References in corpus (12)

• Physics and Mathematics of Calogero particles
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• The quantum harmonic oscillator on the sphere and the hyperbolic plane
• Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
• N=4 superconformal Calogero models
• Calogero models and nonlocal conformal transformations
• Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
• N=4 supersymmetric 3-particles Calogero model
• Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems
• Lobachevsky geometry of (super)conformal mechanics
• A surprise in mechanics with nonlinear chiral supermultiplet

Cited by in corpus (25)

• Superconformal mechanics
• Hidden symmetries of integrable conformal mechanical systems
• Action-angle variables for dihedral systems on the circle
• Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential
• The spherical sector of the Calogero model as a reduced matrix model
• Invariants of the spherical sector in conformal mechanics
• Runge-Lenz vector in Calogero-Coulomb problem
• Spherical Calogero model with oscillator/Coulomb potential: quantum case
• Near-horizon dynamics of particle in extreme Reissner-Nordström and Clément-Gal'tsov black hole backgrounds: action-angle variables
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics
• Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems
• The structure of invariants in conformal mechanics
• On integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions
• Hidden symmetries of the Higgs oscillator and the conformal algebra
• Spherical Calogero model with oscillator/Coulomb potential: classical case
• On the classical and quantum dynamics of a class of nonpolynomial oscillators
• Lobachevsky geometry in TTW and PW systems
• Note on constants of motion in conformal mechanics associated with near horizon extremal Myers-Perry black holes
• Remarks on Multi-Dimensional Conformal Mechanics
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems
• Calogero-like model without rearrangement symmetry
• Coupling and particle number intertwiners in the Calogero model
• The tetrahexahedric Calogero model