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Matthew Durey1, Sam E Turton1, John W M Bush1

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Summary
This summary is machine-generated.

This study explores how self-propelling particles interacting with pilot-wave fields create wavelike motion. Two mechanisms, resonant speed oscillations and random-walk behavior, explain these emergent statistical signatures in dynamical systems.

Keywords:
chaos and nonlinear dynamicsemergent statisticspilot-wave theoryself-propelled particlesstatistical structure

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Area of Science:

  • Theoretical physics
  • Complex systems

Background:

  • Pilot-wave theory describes particle motion guided by a wave field.
  • Understanding emergent statistical signatures is key in dynamical systems.

Purpose of the Study:

  • Investigate mechanisms leading to wavelike statistical signatures in a self-propelling particle-pilot-wave system.
  • Analyze resonant speed oscillations and random-walk behavior.

Main Methods:

  • Theoretical investigation of a dynamical system.
  • Analysis of particle self-propulsion via resonant interaction with a pilot-wave field.
  • Examination of different parameter space regions.

Main Results:

  • Identified two distinct mechanisms for wavelike statistical signatures.
  • Resonant speed oscillations occur when particles are perturbed from steady states.
  • Random-walk-like motion emerges with small pilot-wave field decay rates.

Conclusions:

  • The study rationalizes emergent wavelike statistics in classical pilot-wave systems.
  • Findings provide insights into the complex dynamics of self-propelling particles.
  • The identified mechanisms are crucial for understanding statistical signatures in such systems.