Fractional revivals through R\'enyi uncertainty relations

TL;DR

This paper demonstrates that Reny uncertainty relations effectively describe wave packet dynamics and fractional revivals in quantum systems, offering a robust alternative to traditional methods like the Heisenberg relation and autocorrelation functions.

Contribution

It introduces the use of Reny entropic uncertainty relations as a novel tool for analyzing quantum revival phenomena across multiple model systems.

Findings

Reny relations accurately identify fractional revivals

Entropic uncertainty relations outperform traditional methods in certain contexts

The approach is validated on harmonic oscillator, infinite well, and quantum bouncer

Abstract

We show that the R\'enyi uncertainty relations give a good description of the dynamical behavior of wave packets and constitute a sound approach to revival phenomena by analyzing three model systems: the simple harmonic oscillator, the infinite square well, and the quantum bouncer. We prove the usefulness of entropic uncertainty relations as a tool for identifying fractional revivals by providing a comparison in different contexts with the usual Heisenberg uncertainty relation and with the common approach in terms of the autocorrelation function.