Overload wave-memory induces amnesia of a self-propelled particle

Abstract

Information storage is a key element of autonomous, out-of-equilibrium dynamics, especially for biological and synthetic active matter. In synthetic active matter however, the implementation of internal memory in self-propelled systems is often absent, limiting our understanding of memory-driven dynamics. Recently, a system comprised of a droplet generating its guiding wavefield appeared as a prime candidate for such investigations. Indeed, the wavefield, propelling the droplet, encodes information about the droplet trajectory and the amount of information can be controlled by a single scalar experimental parameter. In this work, we show numerically and experimentally that the accumulation of information in the wavefield induces the loss of time correlations, where the dynamics can then be described by a memory-less process. We rationalize the resulting statistical behavior by defining an effective temperature for the particle dynamics where the wavefield acts as a thermostat of large dimensions, and by evidencing a minimization principle of the generated wavefield.

Pilot-wave dynamics in a rotating frame: the onset of orbital instability

“…an expression proportional to that obtained by Labousse et al (2016b) and Hubert et al (2022), who neglected the contribution of surface tension.…”

“…Owing to the slow spatial decay of the walker wave field (2.1b), the standard wave energy integral diverges when integrating over the plane. Instead, we adopt the notion of wave intensity E, as coined by Hubert et al (2022), which acts as a suitable proxy for the sum of the wave field gravitational potential and surface energies. In dimensional units, we thus define…”

“…To proceed, we deform the integration region to a small region about θ = π, namely π − δ < θ < π + δ with 0 < δ 1, and define The leading-order form of the resultant integral may be determined using method of stationary phase for r 0 1, giving rise to the contribution integral in the radial direction, and taking the limit R → ∞, we obtain (Labousse et al 2016b;Hubert et al 2022)…”

“…Instead, we adopt the notion of wave intensity , as coined by Hubert et al. (2022), which acts as a suitable proxy for the sum of the wave field gravitational potential and surface energies. In dimensional units, we thus define where and are the fluid surface tension coefficient and density, respectively, and has units of energy per unit length.…”

A study discovered the coherent wave function of electrons and the stability when observed

“…In their work, they showed numerically and experimentally that the accumulation of information in the wavefield induces the loss of time correlations, where the dynamics can then be described by a memory-less process. Thus, rationalize the resulting statistical behavior by defining an effective temperature for the particle dynamics where the wavefield acts as a thermostat of large dimensions, and by evidencing a minimization principle of the generated wavefield [4].…”