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

TL;DR

This paper introduces a classical model using $q$-Racah polynomials to achieve perfect pulse transfer and fractional revival in a chain, mimicking quantum spin devices.

Contribution

It presents a novel classical system based on $q$-Racah polynomials that enables dispersionless transfer and fractional revival, expanding the understanding of classical analogs to quantum phenomena.

Findings

Achieves perfect end-to-end pulse transfer in a classical chain.

Demonstrates fractional revival with periodic splitting of momentum.

Provides a classical analog to quantum spin systems with similar transfer properties.

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.