Wave-Like Statistics from Classical Active Particles with Internal Degrees Of Freedom

TL;DR

This paper demonstrates that wave-like spatial patterns in active particles with internal states emerge from their nonlinear dynamics, expanding understanding beyond traditional wave effect explanations.

Contribution

It reveals that wave-like behaviors in active matter can originate from internal nonlinear dynamics rather than nonlocal wave effects, broadening the scope of hydrodynamic quantum analogs.

Findings

Wave-like patterns arise from internal fixed points and chaotic relaxation.

Friedel-like patterns occur in open geometries due to perturbations.

Wave-like structures are observed in confined geometries.

Abstract

Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an inertial active particle with internal degrees of freedom. Steady propulsion corresponds to internal fixed points whose spiral or chaotic relaxation organizes oscillatory ensemble densities. Local perturbations then produce Friedel-like patterns in open geometries and wave-like structure in confined geometries, extending hydrodynamic quantum analogs to inertial active matter more broadly.