Analytic "Newton's cradles" with perfect transfer and fractional revival

TL;DR

This paper introduces analytic mass-spring chains based on para-Racah polynomials that achieve perfect pulse transfer and fractional revival, serving as classical analogs to quantum spin chains for quantum information tasks.

Contribution

It presents a new class of analytic mass-spring chains utilizing para-Racah polynomials for dispersionless transfer and fractional revival, bridging classical and quantum information systems.

Findings

Achieves perfect state transfer in classical mass-spring chains.

Demonstrates fractional revival phenomena in these chains.

Provides a mathematical framework linking classical and quantum systems.

Abstract

Analytic mass-spring chains with dispersionless pulse transfer and fractional revival are presented. These are obtained using the properties of the para-Racah polynomials. This provides classical analogs of the quantum spin chains that realize important tasks in quantum information: perfect state transfer and entanglement generation.