title: 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.
authors.affiliation: Institut Langevin, ESPCI ParisTech, CNRS - UMR 7587, 1 rue Jussieu, 75005 Paris Cedex 05, France, EU.
authors.forename: M
authors.initials: M
authors.lastname: Labousse
authors.affiliation: Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, CNRS - UMR 7057, Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France, EU.
authors.forename: S
authors.initials: S
authors.lastname: Perrard
mesh_terms: D003198:Computer Simulation; D017276:Friction; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D014783:Viscosity