Boomerang effect in classical stochastic models

TL;DR

This paper explores the classical analog of the quantum boomerang effect, demonstrating its presence in classical systems with subdiffusive behavior and linking it to quantum phenomena like Anderson localization.

Contribution

It uncovers the classical boomerang effect in simplified and complex models, expanding understanding of this phenomenon beyond quantum systems.

Findings

Classical systems can exhibit a boomerang-like effect similar to quantum cases.

The effect is associated with systems showing subdiffusive dynamics.

The phenomenon bridges classical and quantum mechanics in disordered media.

Abstract

The phenomenon of Anderson localization, occurring in a disordered medium, significantly influences the dynamics of quantum particles. A fascinating manifestation of this is the "quantum boomerang effect" (QBE), observed when a quantum particle, propelled with a finite initial velocity, reverses its average trajectory, eventually halting at its starting point. This effect has recently been demonstrated in an experiment replicating the quantum kicked-rotor model. This research delves into the classical analog of QBE. We uncover evidence of a similar effect in classical systems, characterized by the absence of typical diffusion processes. Our investigation encompasses both simplified probabilistic models and more complex phenomenological models that link classical with quantum mechanics. The results indicate that the boomerang effect is not confined to the quantum realm and may also be present in diverse systems exhibiting subdiffusive behavior.