Fractional Revival Dynamics in Kerr-Type Systems: Angular Momentum Moments and Classical Analogs

TL;DR

This paper explores fractional revival phenomena in Kerr-type systems, analyzing angular momentum moments and classical analogs to deepen understanding of quantum revivals and their classical counterparts.

Contribution

It introduces explicit expressions for angular momentum moments during fractional revivals and compares quantum revival signatures with classical recurrence behaviors.

Findings

Higher-order angular momentum moments reveal clear signatures of fractional revivals.

Quantum and classical systems exhibit structural similarities in revival and recurrence phenomena.

The study broadens experimental diagnostics for fractional revivals and unifies quantum-classical perspectives.

Abstract

Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier work. In this article, we build on these studies and extend the analysis in two important directions. First, we investigate fractional revival dynamics in angular momentum observables, deriving explicit expressions for the time evolution of their moments and demonstrating that higher-order angular momentum moments provide clear and selective signatures of fractional revivals. Second, we examine classical analogs of quantum revival phenomena and elucidate structural similarities between quantum fractional revivals and recurrence behavior in representative classical systems. Using the Kerr-type nonlinear Hamiltonian as a paradigmatic model, we analyze the autocorrelation function, moment dynamics, and phase-space structures, supported by visualizations such as quantum carpets. Our results broaden the range of experimentally accessible diagnostics of fractional revivals and provide a unified perspective on revival phenomena across quantum and classical dynamical systems.