1 citations · 1 across the 14 of their papers we have counts for
19 papers
Continuous representations of the meta Hahn algebra and special functions
Quentin Labriet, Luc Vinet
Infinite families of biorthogonal rational functions are constructed using infinite dimensional representations of the three-generated meta Hahn algebra. Continuous Hahn and contin…
Para families of orthogonal polynomials
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, -para-Racah and para-Bannai--Ito polynomials followed, obtained…
The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Bannai--Ito polynomials are orthogonal on a Bannai--Ito bi-lattice that is \emph{two-sided} --- it extends on both sides of a central value --- and depend, besides t…
The para--Racah Hamiltonian as an exactly solvable discretization of the Pöschl--Teller box
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter, define through their recurrence relation a mirror-symmetric tridiagonal Hami…
The para--Krawtchouk oscillator and its continuum limit
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that exhibits fractional revival. We determine the continuum limit of this Hami…
A discrete Smorodinsky--Winternitz I superintegrable system
Vutha Vichhea Chea, Luc Vinet
We construct a finite discrete realization of the Smorodinsky--Winternitz I superintegrable system on a triangular region of the two-dimensional square lattice. The construction is…
Universal scaling of spatially extended zero modes in inhomogeneous SSH chains
Gilles Parez, Nicolas Crampé, Quentin Labriet +2
Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this pict…
Morse momentum wavefunctions and rational functions
Luc Vinet, Alexei Zhedanov
We revisit the bound states of the Morse potential in the momentum representation. After the ground-state factor is extracted, the remaining factors are finite rational functions o…
The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra
Vutha Vichea Chea, Luc Vinet, Alexei Zhedanov
We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesia…
Algebraic Leonard trio approach to rational functions: the Hahn case
Nicolas Crampé, Quentin Labriet, Lucia Morey +1
The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn a…
The dynamical algebra of the generic superintegrable model on the two-sphere
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of…
Meta Algebras and Special Functions: the Racah Case
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its…
Ruijsenaars-van Diejen-Takemura Hamiltonians as rational Heun operators
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The most general Ruijsenaars-van Diejen-Takemura Hamiltonians are characterized as Heun operators defined as second order -difference operators with a raising action on elementa…
Bispectral rational functions and Leonard trios
Nicolas Crampé, Wolter Groenevelt, Quentin Labriet +3
It is well-known that Leonard pairs have a close connection with bispectral orthogonal polynomials of the Askey scheme. In this paper, we introduce the notion of a Leonard trio $(V…
Inhomogeneous SSH models and the doubling of orthogonal polynomials
Nicolas Crampé, Quentin Labriet, Lucia Morey +2
We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of th…
Algebraic interpretation of discrete families of matrix valued orthogonal polynomials
Quentin Labriet, Lucia Morey, Luc Vinet
An algebraic interpretation of matrix-valued orthogonal polynomials (MVOPs) is provided. The construction is based on representations of a (-deformed) Lie algebra …
Algebraic interpretation of the two-variable Jacobi polynomials on the triangle: the pentagonal way
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is used to provide an interpretation of the two-variable Jacobi polynomials on the triangle, as overlaps betwee…
symmetry of XX spin chains
Nicolas Crampé, Rafael I. Nepomechie, Luc Vinet +1
We show that, after suitably adjusting a uniform transverse magnetic field, the generic inhomogeneous open XX spin chain has a two-fold degeneracy, and an exact symmetry wh…
Algebras behind the bispectrality of the Wilson rational functions and their limits
Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet +1
The properties of the Wilson rational functions with three different normalizations are described. For one normalization, it satisfies an recurrence relation,…