Non-Hamiltonian features of a classical pilot-wave dynamics

Abstract

A bouncing droplet on a vibrated bath can couple to the waves it generates, so that it becomes a propagative walker. Its propulsion at constant velocity means that a balance exists between the permanent input of energy provided by the vibration and the dissipation. Here we seek a simple theoretical description of the resulting non-Hamiltonian dynamics with a walker immersed in a harmonic potential well. We demonstrate that the interaction with the recently emitted waves can be modeled by a Rayleigh-type friction. The Rayleigh oscillator has well defined attractors. The convergence toward them and their stability is investigated through an energetic approach and a linear stability analysis. These theoretical results provide a description of the dynamics in excellent agreement with the experimental data. It is thus a basic framework for further investigations of wave-particle interactions when memory effects are included.

10 pages, 6 figures

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Cited by in corpus (9)

• Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits
• Interaction of two walkers: Wave-mediated energy and force
• Build-up of macroscopic eigenstates in a memory-based constrained system
• Strings of droplets propelled by coherent waves
• Hydrodynamic superradiance in wave-mediated cooperative tunneling
• Self-propulsion and crossing statistics under random initial conditions
• Neimark--Sacker bifurcation and evidence of chaos in a discrete dynamical model of walkers
• Walking Droplets Through the Lens of Dynamical Systems
• Overload wave-memory induces amnesia of a self-propelled particle