Unsteady dynamics of a classical particle-wave entity

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.

arXiv comment18 pages, 12 figures

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Cited by in corpus (10)

• Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
• Attractor-driven matter
• Anomalous transport of a classical wave-particle entity in a tilted potential
• Pseudo-laminar chaos from on-off intermittency
• Overload wave-memory induces amnesia of a self-propelled particle
• Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
• Quantum-like behavior of an active particle in a double-well potential
• Statistical self-organization of a gas of interacting walking drops in a confining potential
• Damped-driven system of bouncing droplets leading to deterministic diffusive behavior
• Markovian Embedding of Nonlinear Memory via Spectral Representation