A classical model for perfect transfer and fractional revival based on $q$-Racah polynomials

Abstract

It is shown how choices based on the $q$-Racah polynomials for the masses and spring constants along a chain give new systems that exactly allow dispersionless end-to-end transmission of a pulse as well as periodic splitting of the initial momentum between the first and last mass. This ``Newton's cradle'' provides a classical analog of quantum spin devices that exhibit perfect state transfer and fractional revival.

11 pages

References in corpus (6)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• Quantum state transfer in spin chains with q-deformed interaction terms
• Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains
• Dispersionless pulse transport in mass-spring chains: All possible perfect Newton's cradles
• Analytic "Newton's cradles" with perfect transfer and fractional revival

Cited by in corpus (1)

• Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer