Walking droplets in a circular corral: Quantisation and chaos

Area of Science:

• Fluid dynamics
• Wave phenomena
• Quantum mechanics analogies

Background:

• Millimetric liquid droplets can "walk" on vibrating liquid surfaces.
• These "walkers" mimic quantum behaviors, such as wave-particle duality.
• Confined walkers display statistical behaviors analogous to quantum systems.

Purpose of the Study:

• To experimentally investigate the dynamics of a walking droplet within a circular corral.
• To characterize the emergence of stable dynamical states and their quantization.
• To examine the transition to chaos and the breakdown of quantization with increasing vibrational acceleration.

Main Methods:

• Experimental observation of a millimetric walking droplet in a circular confinement.
• Systematic variation of vibrational acceleration to study dynamical transitions.
• Analysis of droplet trajectories, angular momentum, and orbital radius.

Main Results:

• Emergence of stable dynamical states with double quantization of angular momentum and orbital radius at low accelerations.
• Characterization of the transition to chaos as vibrational acceleration increases.
• Observation of the breakdown of double quantization in the chaotic regime.

Conclusions:

• Walking droplet dynamics in a circular corral exhibit quantized states analogous to quantum systems.
• The system transitions from regular, quantized motion to chaotic behavior with increasing driving force.
• This provides a macroscopic analog for exploring quantum phenomena and chaos theory.