Unsteady dynamics of a classical particle-wave entity

TL;DR

This paper investigates the unsteady behaviors of a classical particle-wave system modeled after bouncing droplets, revealing complex dynamics including steady, oscillating, and irregular motions, and establishing links to well-known dynamical systems.

Contribution

It introduces a generalized one-dimensional pilot-wave model to analyze the effects of wave form variations on particle dynamics, highlighting new unsteady behaviors and their theoretical connections.

Findings

Identification of steady and unsteady walking motions

Discovery of irregular walking linked to Lorenz system dynamics

Connections made between droplet behavior, Langevin equation, and deterministic diffusion

Abstract

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.