Non-Hamiltonian features of a classical pilot-wave dynamics

Area of Science:

• Fluid dynamics
• Wave-particle interactions
• Non-Hamiltonian dynamics

Background:

• Bouncing droplets on vibrated baths exhibit wave-particle coupling, leading to self-propelled walker behavior.
• This propulsion implies a balance between energy input from vibrations and energy dissipation.
• Understanding the underlying non-Hamiltonian dynamics is crucial for wave-particle interaction studies.

Purpose of the Study:

• To develop a simple theoretical description for the dynamics of a bouncing droplet walker in a harmonic potential well.
• To model the interaction between the droplet and its generated waves using a Rayleigh-type friction.
• To investigate the convergence and stability of the system's attractors.

Main Methods:

• Theoretical modeling of droplet-wave interaction as Rayleigh friction.
• Energetic approach to analyze convergence towards attractors.
• Linear stability analysis to determine attractor stability.

Main Results:

• The droplet-wave interaction can be effectively modeled by Rayleigh friction.
• The Rayleigh oscillator model exhibits well-defined attractors.
• Theoretical predictions show excellent agreement with experimental data regarding droplet dynamics.

Conclusions:

• The Rayleigh friction model provides a basic framework for understanding bouncing droplet walker dynamics.
• This framework accurately describes wave-particle interactions, including energy dissipation and stability.
• The study lays the groundwork for future investigations incorporating memory effects in wave-particle interactions.