10 citations · 38 across the 24 of their papers we have counts for
26 papers
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…
Polynomials of the Askey Scheme as Clebsch-Gordan Coefficients
Nicolas Crampé, Loïc Poulain d'Andecy, Luc Vinet
Given a semi-simple algebra equipped with a coproduct, the Clebsch-Gordan coefficients are the elements of the transition matrices between direct product representation and its irr…
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…
Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
Pierre-Antoine Bernard, Rafael I. Nepomechie, Gilles Parez +3
In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading…
Contiguity relations for finite families of orthogonal polynomials in the Askey scheme
Nicolas Crampé, Lucia Morey, Luc Vinet +1
This paper classifies the contiguity relations for finite families of polynomials within the (-)Askey scheme. The necessary and sufficient conditions for the existence of these…
A dynamical algebra of protocol-induced transformations on Dicke states
Pierre-Antoine Bernard, Luc Vinet
Quantum -qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Conse…
Entanglement Hamiltonian and orthogonal polynomials
Pierre-Antoine Bernard, Riccarda Bonsignori, Viktor Eisler +2
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the singl…
Distinctive features of inhomogeneous spin chains
Pierre-Antoine Bernard, Gilles Parez, Luc Vinet
This review presents recent developments in the study of inhomogeneous XX spin chains, highlighting results on perfect state transfer, out-of-equilibrium stationary dynamics in ope…
Meta algebras and biorthogonal rational functions: the -Hahn case
Pierre-Antoine Bernard, Abderahmane Bouziane, Samuel Pellerin +5
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of -Hahn type is provided. The approach relies on the me…
A tale of two -deformations : connecting dual polar spaces and weighted hypercubes
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
Two -analogs of the hypercube graph are introduced and shown to be related through a graph quotient. The roles of the subspace lattice graph, of a twisted primitive elements of…
A -version of the relation between the hypercube, the Krawtchouk chain and Dicke states
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
It is shown how the spin chain based on the dual -Krawtchouk polynomials is connected to a weighted hypercube through the use of -Dicke states. The representation theoretic u…
Currents in non-equilibrium steady states of open inhomogeneous -spin chains
Pierre-Antoine Bernard, Ismaël Bussière, Roberto Floreanini +1
We investigate spin and heat currents in the non-equilibrium steady state of inhomogeneous -spin chains, which act as interfaces between two bosonic heat baths. Using special f…
Fermionic logarithmic negativity in the Krawtchouk chain
Gabrielle Blanchet, Gilles Parez, Luc Vinet
The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawt…
Bivariate - and -polynomial structures of the association schemes based on attenuated spaces
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet +2
The bivariate - and -polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomia…
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…
Entanglement of free-fermion systems, signal processing and algebraic combinatorics
Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie +2
This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic comb…
-Griffiths polynomials: Bispectrality and biorthogonality
N. Crampe, L. Frappat, J. Gaboriaud +3
We introduce a generalization of bivariate Griffiths polynomials depending on an additional parameter . These -Griffiths polynomials are bivariate, bispectral and biorthogona…
m-distance-regular graphs and their relation to multivariate P-polynomial association schemes
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet +2
An association scheme is -polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate -polynomial association schemes of t…
Superspace realizations of the Bannai-Ito algebra
N. Crampe, H. De Bie, P. Iliev +1
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra in te…
Bivariate -polynomial association schemes
P. -A. Bernard, N. Crampe, L. Poulain d'Andecy +2
Bivariate P-polynomial association scheme of type are defined as a generalization of the P-polynomial association schemes. This generalization is shown to be equivalent to…
Askey-Wilson braid algebra and centralizer of
Nicolas Crampe, Loic Poulain d'Andecy, Luc Vinet +1
A presentation of the centralizer of the three-fold tensor product of the spin representation of the quantum group is provided. It is expressed as a quot…