Chaos driven by interfering memory

Abstract

The transmission of information can couple two entities of very different nature, one of them serving as a memory for the other. Here we study the situation in which information is stored in a wave field and serves as a memory that pilots the dynamics of a particle. Such a system can be implemented by a bouncing drop generating surface waves sustained by a parametric forcing. The motion of the resulting "walker" when confined in a harmonic potential well is generally disordered. Here we show that these trajectories correspond to chaotic regimes characterized by intermittent transitions between a discrete set of states. At any given time, the system is in one of these states characterized by a double quantization of size and angular momentum. A low dimensional intermittency determines their respective probabilities. They thus form an eigenstate basis of decomposition for what would be observed as a superposition of states if all measurements were intrusive.

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Cited by in corpus (24)

• Superwalking droplets
• Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits
• Build-up of macroscopic eigenstates in a memory-based constrained system
• Faraday instability and subthreshold Faraday waves: surface waves emitted by walkers
• Multi-stable free states of an active particle from a coherent memory dynamics
• Tunable bimodal explorations of space from memory-driven deterministic dynamics
• Unsteady dynamics of a classical particle-wave entity
• Hong-Ou-Mandel-like two-droplet correlations
• Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity
• Transition to chaos in wave memory dynamics in a harmonic well : deterministic and noise-driven behaviour
• Neimark--Sacker bifurcation and evidence of chaos in a discrete dynamical model of walkers
• Self-propulsion and crossing statistics under random initial conditions
• Equivalent quantum equations in a system inspired by bouncing droplets experiments
• Pilot-wave dynamics of two identical, in-phase bouncing droplet
• Emergence of superwalking droplets
• Are Hidden-Variable Theories for Pilot-Wave Systems Possible ?
• Anomalous transport of a classical wave-particle entity in a tilted potential
• Pseudo-laminar chaos from on-off intermittency
• Overload wave-memory induces amnesia of a self-propelled particle
• Dynamics, interference effects, and multistability in a Lorenz-like system of a classical wave-particle entity in a periodic potential
• Stop-and-go locomotion of superwalking droplets
• Crises and chaotic scattering in hydrodynamic pilot-wave experiments
• Statistical self-organization of a gas of interacting walking drops in a confining potential
• The invariant measure of a walking droplet in hydrodynamic pilot-wave theory