Non-Hamiltonian features of a classical pilot-wave dynamics

Matthieu Labousse (1) , Stéphane Perrard (2)

1 IL - Institut Langevin - Ondes et Images (UMR7587)
2 MSC - Matière et Systèmes Complexes

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.

Mots clés: Rayleigh oscillator; boucing drops; harmonic potential

Domaines: Physique Classique [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]

Matthieu Labousse, Stéphane Perrard. Non-Hamiltonian features of a classical pilot-wave dynamics. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 90, pp.022913. ⟨10.1103/PhysRevE.90.022913⟩. ⟨hal-01059409⟩