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A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials
Vincent X. Genest, Hiroshi Miki, Luc Vinet +1
A simple discrete model of the two dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help…
The Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
Hendrik De Bie, Vincent X. Genest, Luc Vinet
The kernel of the Dirac-Dunkl operator is examined. The symmetry algebra of the associated Dirac-Dunkl equation on is determ…
Quantum spin chains with fractional revival
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
A systematic study of fractional revival at two sites in quantum spin chains is presented and analytic models with this phenomenon are exhibited. The generic models have two e…
Exact Fractional Revival in Spin Chains
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained tha…
Generating functions for the osp(1|2) Clebsch-Gordan coefficients
Geoffroy Bergeron, Luc Vinet
Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generatin…
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard r…