Build-up of macroscopic eigenstates in a memory-based constrained system

TL;DR

This paper develops a theoretical framework for walker dynamics influenced by memory effects, explaining the emergence of macroscopic structures and organization in a confined system under external potential.

Contribution

It introduces a novel time scale decomposition approach to model the multi-scale effects of memory in walker dynamics and self-organization.

Findings

Short time scale drives propulsion.

Intermediate scale creates pivotal structures with angular momentum.

Large memory scale leads to global self-organization.

Abstract

A bouncing drop and its associated accompanying wave forms a walker. Based on previous works, we show in this article that it is possible to formulate a simple theoretical framework for the walker dynamics. It relies on a time scale decomposition corresponding to the effects successively generated when the memory effects increase. While the short time scale effect is simply responsible for the walker's propulsion, the intermediate scale generates spontaneously pivotal structures endowed with angular momentum. At an even larger memory scale, if the walker is spatially confined, the pivots become the building blocks of a self-organization into a global structure. This new theoretical framework is applied in the presence of an external harmonic potential, and reveals the underlying mechanisms leading to the emergence of the macroscopic spatial organization reported by Perrard et al. (2014, Nature Commun. 5, 3219)