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

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.

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

“…Furthermore, r cannot be equal to 1 according to (59) implying that τ 1,r t * . This observation that FR will always occur contrasts with the other classical models analysed so far [14,20], which could give rise to systems with perfect transfer only, without FR.…”

“…The first system [14] is associated to the dual Hahn polynomials and exhibits perfect return. This mass-spring chain was shown in [20] to be a special case of models based on the para-Racah polynomials and these more general chains were found to have both perfect transfer and fractional revival.…”

“…The classical enactment of fractional revival was looked at recently in [20] where are presented massspring chains showing periodical dispersionless distribution to the first and last masses only, of the momentum initially given to the first mass. As a matter of fact, we called upon the para-Racah polynomials to obtain such analytic systems that have in some cases both perfect transfer and fractional revival and in other cases 1 only the latter.…”