7 papers · 1 filter
A discrete Smorodinsky--Winternitz II superintegrable system
Pierre-Antoine Bernard, Vutha Vichhea Chea, Luc Vinet
We construct a discrete Smorodinsky--Winternitz II superintegrable system on a triangular region of the two-dimensional square lattice. The model is built from a pair of commuting…
Realization embeddings of the rank two Racah algebra into the rank two Jacobi algebra
Nicolas Crampé, Sarah Post, Luc Vinet
We construct an explicit embedding of the rank two Racah algebra into the rank two Jacobi algebra . Working in the differential model of $\mathfrak…
Rational Heun operators on -linear grids
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Rational Heun operators on the linear grid are presented. They are second-order difference operators constructively defined from the requirement that they have a rais…
Perfect state transfer in inhomogeneous XX model of q-Racah type
Nicolas Crampe, Simon Lafrance, Charles Robillard +1
New exactly solvable one-dimensional XX spin chain models that exhibit perfect state transfer are defined. These models have inhomogeneous couplings and magnetic fields determined…
Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet +2
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jorda…
Griffiths polynomials of Racah type
Nicolas Crampe, Luc Frappat, Julien Gaboriaud +3
Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the l…