Information stored in Faraday waves: the origin of a path memory

Abstract

On a vertically vibrating fluid interface, a droplet can remain bouncing indefinitely. When approaching the Faraday instability onset, the droplet couples to the wave it generates and starts propagating horizontally. The resulting wave–particle association, called a walker, was shown previously to have remarkable dynamical properties, reminiscent of quantum behaviours. In the present article, the nature of a walker's wave field is investigated experimentally, numerically and theoretically. It is shown to result from the superposition of waves emitted by the droplet collisions with the interface. A single impact is studied experimentally and in a fluid mechanics theoretical approach. It is shown that each shock emits a radial travelling wave, leaving behind a localized mode of slowly decaying Faraday standing waves. As it moves, the walker keeps generating waves and the global structure of the wave field results from the linear superposition of the waves generated along the recent trajectory. For rectilinear trajectories, this results in a Fresnel interference pattern of the global wave field. Since the droplet moves due to its interaction with the distorted interface, this means that it is guided by a pilot wave that contains a path memory. Through this wave-mediated memory, the past as well as the environment determines the walker's present motion.

Simulations of pilot-wave dynamics in a simple harmonic potential

“…The lifetime of these waves increases as γ approaches γ F and is prescribed by the memory parameter M e = T d /T F (1 − γ /γ F ), where T d is the decay time of the waves in the absence of forcing and T F is the Faraday period. Thus, the walker has an associated path memory that increases as γ approaches γ F [5].…”

Exotic states of bouncing and walking droplets

“…[3][4][5] Second, in certain parameter regimes, the bouncers walk horizontally through resonant interaction with their wave field. [6][7][8][9][10] The resulting walkers represent the first known example of a macroscopic pilot-wave system, [11][12][13] and exhibit many features thought to be exclusive to the microscopic quantum realm, 14 including self-organising lattice structures, 15,16 single particle diffraction, 17 quantized orbits, 18 orbital level splitting, 19 tunneling effects, 20 and wave-like statistics in confined geometries. 21 Consider a fluid of density ρ, kinematic viscosity ν, and surface tension σ in a horizontal bath of depth H driven by a vertical vibration of amplitude A and frequency f = ω/(2π ).…”

“…1), there are three basic outcomes: the droplet may either coalesce, bounce in place, or walk across the fluid surface. 1,7,9 For γ < γ B , where γ B is the bouncing threshold, the applied forcing is insufficient to levitate the drop, which then settles towards the bath. The intervening air layer thins until reaching a critical thickness at which Van der Waals forces between drop and bath initiate coalescence.…”

“…[7][8][9] Protiere et al 7 conducted experiments with a viscosity-frequency combination of 50 cS-50 Hz and summarised their results in a regime diagram illustrating the droplet behaviour in the D-plane. For low forcing accelerations, simple bouncing arises: the drop hits the bath once every driving period.…”

Links between fluid mechanics and quantum mechanics: a model for information in economics?

“…In this section, we actually consider a macroscopic version of a model which is steeped in quantum mechanics. The model which will be discussed is also supported by experimental evidence (see [38][39][40][41][42]). …”