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Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits.
M Labousse1,2, A U Oza3, S Perrard2
1Institut Langevin, ESPCI Paristech, CNRS, UMR No. 7587, PSL Research University, Université Pierre and Marie Curie, 1 Rue Jussieu, 75005 Paris, France, EU.
Physical Review. E
|April 15, 2016
Summary
Walking droplets on vibrating fluid baths exhibit stable orbital motion under harmonic potentials. Theoretical models accurately predict orbital radius, frequency, and stability, aligning with experimental observations.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Wave Phenomena
Background:
- Walking droplets on fluid baths are a model system for wave-particle duality.
- Previous studies have explored droplet behavior under various external forces.
- Understanding droplet dynamics is crucial for fluid mechanics and quantum analogies.
Purpose of the Study:
- To theoretically investigate the dynamics of a walking droplet under a harmonic potential.
- To describe the droplet's horizontal motion using an integro-differential equation.
- To analyze and predict orbital solutions, quantization, and stability.
Main Methods:
- Developed a theoretical model using an integro-differential trajectory equation.
- Derived steady orbital solutions for the walking droplet.
- Analyzed orbital quantization and stability based on theoretical predictions.
Main Results:
- Identified steady orbital solutions for the walking droplet's motion.
- Predicted the dependence of orbital radius and frequency on harmonic force strength.
- Rationalized orbital quantization and compared stability predictions with experimental data.
Conclusions:
- The theoretical model accurately describes walking droplet dynamics under harmonic potentials.
- Favorable agreement between theoretical predictions and experimental data validates the model.
- The study provides insights into orbital quantization and stability in this system.
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