Nicolas Crampé
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View article: Perfect state transfer in inhomogeneous XX model of q-Racah type
Perfect state transfer in inhomogeneous XX model of q-Racah type Open
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 from the three-term recurrence relations satisfied by the q…
View article: Exactly solvable inhomogeneous <i>XY</i> spin chain
Exactly solvable inhomogeneous <i>XY</i> spin chain Open
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 Jordan–Wigner transformation. Finding the spectrum of such model…
View article: $su(2)$ symmetry of XX spin chains
$su(2)$ symmetry of XX spin chains Open
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 $su(2)$ symmetry whose "inhomogeneous" nonlocal generators depend on coefficie…
View article: Change of basis for tridiagonal pairs of type II
Change of basis for tridiagonal pairs of type II Open
View article: The rank two Jacobi algebra
The rank two Jacobi algebra Open
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of ra…
View article: Exactly solvable inhomogeneous XY spin chain
Exactly solvable inhomogeneous XY spin chain Open
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 Jordan-Wigner transformation. Finding the spectrum of such model…
View article: <i>λ</i>-Griffiths polynomials: Bispectrality and biorthogonality
<i>λ</i>-Griffiths polynomials: Bispectrality and biorthogonality Open
We introduce a generalization of bivariate Griffiths polynomials depending on an additional parameter λ. These λ-Griffiths polynomials are bivariate, bispectral and biorthogonal. For two specific values of the parameter λ, they become orth…
View article: Algebras behind the bispectrality of the Wilson rational functions and their ${}_4ϕ_3$ limits
Algebras behind the bispectrality of the Wilson rational functions and their ${}_4ϕ_3$ limits Open
The properties of the Wilson rational functions ${}_{10}ϕ_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a generalized…
View article: Factorized $$A_2$$-Leonard pair
Factorized $$A_2$$-Leonard pair Open
View article: Bivariate P- and Q-polynomial structures of the association schemes based on attenuated spaces
Bivariate P- and Q-polynomial structures of the association schemes based on attenuated spaces Open
View article: Griffiths polynomials of Racah type
Griffiths polynomials of Racah type Open
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 latter. A duality relation and the orthogonality of these po…
View article: m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes
m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes Open
View article: Bivariate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>-polynomial association schemes
Bivariate -polynomial association schemes Open
Bivariate -polynomial association scheme of type are defined as a generalization of the -polynomial association schemes. This generalization is shown to be equivalent to a set of conditions on the intersection parameters. A number of know…
View article: Entanglement of free-fermion systems, signal processing and algebraic combinatorics
Entanglement of free-fermion systems, signal processing and algebraic combinatorics Open
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 combinatorics. On the one hand, a parallel with time and band l…
View article: Factorized $A_2$-Leonard pair
Factorized $A_2$-Leonard pair Open
The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions a…
View article: Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz Open
The computation of the entanglement entropy for inhomogeneous free fermions chains based on q-Racah polynomials is considered. The eigenvalues of the truncated correlation matrix are obtained from the diagonalization of the associated Heun…
View article: Matrix elements of <i>SO</i>(3) in <i>sl</i>3 representations as bispectral multivariate functions
Matrix elements of <i>SO</i>(3) in <i>sl</i>3 representations as bispectral multivariate functions Open
We compute the matrix elements of SO(3) in any finite-dimensional irreducible representation of sl3. They are expressed in terms of a double sum of products of Krawtchouk and Racah polynomials which generalize the Griffiths–Krawtchouk poly…
View article: A bivariate Q-polynomial structure for the non-binary Johnson scheme
A bivariate Q-polynomial structure for the non-binary Johnson scheme Open
View article: The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms
The Higher-Rank Askey-Wilson Algebra and Its Braid Group Automorphisms Open
We propose a definition by generators and relations of the rank $n-2$ Askey-Wilson algebra $\mathfrak{aw}(n)$ for any integer $n$, generalising the known presentation for the usual case $n=3$. The generators are indexed by connected subset…
View article: Superspace realizations of the Bannai–Ito algebra
Superspace realizations of the Bannai–Ito algebra Open
View article: m-distance-regular graphs and their relation to multivariate P-polynomial association schemes
m-distance-regular graphs and their relation to multivariate P-polynomial association schemes Open
An association scheme is $P$-polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate $P$-polynomial association schemes of type $(α,β)$ were introduced by Bernard et al., and multivar…
View article: Matrix elements of $SO(3)$ in $sl_3$ representations as bispectral multivariate functions
Matrix elements of $SO(3)$ in $sl_3$ representations as bispectral multivariate functions Open
We compute the matrix elements of $SO(3)$ in any finite-dimensional irreducible representation of $sl_3$. They are expressed in terms of a double sum of products of Krawtchouk and Racah polynomials which generalize the Griffiths-Krawtchouk…
View article: A bivariate $Q$-polynomial structure for the non-binary Johnson scheme
A bivariate $Q$-polynomial structure for the non-binary Johnson scheme Open
The notion of multivariate $P$- and $Q$-polynomial association scheme has been introduced recently, generalizing the well-known univariate case. Numerous examples of such association schemes have already been exhibited. In particular, it h…
View article: Entanglement of free fermions on Johnson graphs
Entanglement of free fermions on Johnson graphs Open
Free fermions on Johnson graphs J(n, k) are considered, and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irre…
View article: An Explanation of the Commuting Operator “Miracle” in Time and Band Limiting
An Explanation of the Commuting Operator “Miracle” in Time and Band Limiting Open
View article: Multipartite information of free fermions on Hamming graphs
Multipartite information of free fermions on Hamming graphs Open
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View article: Report on scipost_202212_00041v1
Report on scipost_202212_00041v1 Open
The computation of the entanglement entropy for inhomogeneous free fermions chains based on q-Racah polynomials is considered.The eigenvalues of the truncated correlation matrix are obtained from the diagonalization of the associated Heun …
View article: The Missing Label of $$\mathfrak {su}_3$$ and Its Symmetry
The Missing Label of $$\mathfrak {su}_3$$ and Its Symmetry Open
View article: Bethe ansatz diagonalization of the Heun–Racah operator
Bethe ansatz diagonalization of the Heun–Racah operator Open
View article: Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
Nonlinear Schrödinger equation on the half-line without a conserved number of solitons Open