State space geometry of the chaotic pilot-wave hydrodynamics

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Chaos theory

Background:

• Bouncing droplet systems exhibit complex behaviors on vibrating fluid surfaces.
• Pilot-wave systems, inspired by quantum mechanics, offer a framework for studying droplet dynamics.
• Understanding chaotic regimes and attractors is crucial for predicting system evolution.

Purpose of the Study:

• To develop a rotation symmetry-reduced model for droplet bouncing on a vibrating bath with a central potential.
• To apply dynamical systems theory tools to analyze the reduced model.
• To investigate the onset and progression of chaos, including the formation of a global attractor.

Main Methods:

• Formulation of a rotation symmetry-reduced description of the droplet-bath system.
• Application of dynamical systems theory to identify bifurcations and chaotic regions.
• Analysis of a specific model: pilot-wave system with a central harmonic force.

Main Results:

• Identification of local bifurcations and the initial onset of chaos.
• Description of chaotic region emergence and merging bifurcations.
• Observation of a global attractor where the droplet's angular momentum spontaneously reverses sign.

Conclusions:

• Symmetry reduction provides an effective method for analyzing complex droplet dynamics.
• The model successfully reproduces experimental observations of spontaneous angular momentum sign changes.
• The study elucidates the pathway to chaos and global attractors in this fluid system.