Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

Abstract

We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.

References in corpus (8)

• Path-memory induced quantization of classical orbits
• Self-organization into quantized eigenstates of a classical wave driven particle
• Numerical simulation of Faraday waves
• Chaos driven by interfering memory
• Resonant and rolling droplet
• About the lifetime of a bouncing droplet
• Build-up of macroscopic eigenstates in a memory-based constrained system
• Non-Hamiltonian features of a classical pilot-wave dynamics

Cited by in corpus (11)

• Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers
• Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
• Transition to chaos in wave memory dynamics in a harmonic well : deterministic and noise-driven behaviour
• Emergence of superwalking droplets
• Bouncing oil droplets, de Broglie's quantum thermostat and convergence to equilibrium
• Non-resonant effects in pilot-wave hydrodynamics
• Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
• Quantum-like behavior of an active particle in a double-well potential
• Statistical self-organization of a gas of interacting walking drops in a confining potential
• The invariant measure of a walking droplet in hydrodynamic pilot-wave theory
• A synchrotron-like pumped ring resonator for water waves