Interaction of two walkers: Wave-mediated energy and force

Abstract

A bouncing droplet, self-propelled by its interaction with the waves it generates, forms a classical wave-particle association called a "walker." Previous works have demonstrated that the dynamics of a single walker is driven by its global surface wave field that retains information on its past trajectory. Here, we investigate the energy stored in this wave field for two coupled walkers and how it conveys an interaction between them. For this purpose, we characterize experimentally the "promenade modes" where two walkers are bound, and propagate together. Their possible binding distances take discrete values, and the velocity of the pair depends on their mutual binding. The mean parallel motion can be either rectilinear or oscillating. The experimental results are recovered analytically with a simple theoretical framework. A relation between the kinetic energy of the droplets and the total energy of the standing waves is established.

arXiv comment11 pages, 8 figures

References in corpus (3)

• Path-memory induced quantization of classical orbits
• Self-organization into quantized eigenstates of a classical wave driven particle
• Non-Hamiltonian features of a classical pilot-wave dynamics

Cited by in corpus (13)

• Superwalking droplets
• Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers
• Strings of droplets propelled by coherent waves
• Collective vibrations of confined levitating droplets
• Hong-Ou-Mandel-like two-droplet correlations
• Equivalent quantum equations in a system inspired by bouncing droplets experiments
• Walking Droplets Through the Lens of Dynamical Systems
• Pilot-wave dynamics of two identical, in-phase bouncing droplet
• Statistical self-organization of a gas of interacting walking drops in a confining potential
• Wave-particle duality coming from a bead oscillator in an elastic medium, theoretical study and quantum similarities
• Bragg's reflection for walking droplets in 1D crystals
• Effective gravity and effective quantum equations in a system inspired by walking droplets experiments
• Multi-bounce resonances in the interaction of walking droplets