Dual -1 Hahn polynomials and perfect state transfer

Abstract

We find all the $XX$ spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials $R_n(x;\alpha ,\beta ,N)$. For $N$ odd we recover a model that had already been identified while for $N$ even, we obtain a new system exhibiting PST.

11 pages

References in corpus (5)

• Mirror Inversion of Quantum States in Linear Registers
• How to construct spin chains with perfect state transfer
• Dunkl shift operators and Bannai-Ito polynomials
• An Exactly Solvable Spin Chain Related to Hahn Polynomials
• Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality

Cited by in corpus (9)

• How to construct spin chains with perfect state transfer
• Quantum spin chains with fractional revival
• Bispectrality of the Complementary Bannai-Ito Polynomials
• Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
• Exact Fractional Revival in Spin Chains
• A classical model for perfect transfer and fractional revival based on $q$-Racah polynomials
• Perfect State Transfer in a Spin Chain without Mirror Symmetry
• Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
• Convolution identities for Dunkl orthogonal polynomials from the $\mathfrak{osp}(1|2)$ Lie superalgebra