Recurrence properties of quantum observables in wave packet dynamics

TL;DR

This paper explores the recurrence behavior of quantum observables in wave packet dynamics, revealing how nonlinearity and initial state coherence influence the transition from quasiperiodic to chaotic behavior in quantum systems.

Contribution

It introduces a detailed analysis of recurrence properties in quantum systems, linking recurrence-time distributions to dynamical regimes like chaos and quasiperiodicity.

Findings

Recurrence-time distributions vary from quasiperiodic to hyperbolic depending on system parameters.

Chaotic evolution correlates with exponential recurrence-time distributions and positive Lyapunov exponents.

The study connects quantum recurrence properties with classical dynamical concepts.

Abstract

We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time distributions, return maps and recurrence plots, we conclude that the dynamics of appropriate observables pertaining to the field can vary from quasiperiodicity to hyperbolicity, depending on the extent of the nonlinearity and of the departure from coherence of the initial state of the field. We establish that, in a simple bipartite model in which the field is effectively an open quantum system, a decaying exponential recurrence-time distribution, characteristic of a hyperbolic dynamical system, is associated with chaotic temporal evolution as characterized by a positive Liapunov exponent.