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Walking droplets in a circular corral: Quantisation and chaos.

Tudor Cristea-Platon1, Pedro J Sáenz1, John W M Bush1

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Millimetric walking droplets exhibit quantum-like behaviors. This study explores their dynamics in a circular corral, revealing quantized states and chaotic transitions, offering insights into wave-particle duality analogies.

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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.