Identifying wave packet fractional revivals by means of information entropy

TL;DR

This paper demonstrates that the sum of information entropies in position and momentum spaces effectively indicates wave packet fractional revivals across various physical systems, offering a complementary approach to traditional autocorrelation methods.

Contribution

It introduces the use of information entropy sums as a novel indicator for fractional revivals in wave packet dynamics, validated across multiple models.

Findings

Entropy sums signal fractional revivals clearly.

Method applies to diverse physical systems.

Complementary to autocorrelation function analysis.

Abstract

Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and momentum conjugate spaces is an indicator of fractional revivals by analyzing three different model systems: $(i)$ the infinite square well, $(ii)$ a particle bouncing vertically against a wall in a gravitational field, and $(iii)$ the vibrational dynamics of hydrogen iodide molecules. This description in terms of information entropies complements the usual one in terms of the autocorrelation function.