Collective dynamics of trail-interacting particles

TL;DR

This paper introduces a minimal model for trail-interacting particles that reveals how memory effects and fluctuations lead to novel collective behaviors like superdiffusion, clustering, and condensation.

Contribution

The study develops a stochastic density functional theory for trail-interacting particles, extending understanding from single-particle to collective dynamics with persistent memory fields.

Findings

Repulsive trails cause superdiffusive spreading and transient clustering.

Attractive trails lead to finite-time condensation into localized states.

Memory effects fundamentally alter collective behaviors in trail-interacting systems.

Abstract

Trail interactions occur when past particle trajectories bias future motion, rendering the system out of thermodynamic equilibrium. While such systems are abundant in nature, their understanding is limited to the single-particle level or phenomenological mean-field theories. Here, we introduce a minimal model of many trail-interacting particles that extends this paradigm to the fluctuating collective level. Particles diffuse while depositing long-lasting repelling/attracting trails that act as a shared memory field, coupling their dynamics across time and space. Using stochastic density functional theory, we derive fluctuating hydrodynamic equations and analyze analytically and numerically the resulting behaviors. We show that memory, coupled with fluctuations, fundamentally reshapes collective dynamics; In the repulsive case, the particle density displays superdiffusive spreading characterized by transient clustering and ballistic motion; In the attractive case, the system condensates in finite time into frozen, localized states. Our results establish general principles for trail-interacting systems and reveal how persistent fields generate novel instabilities and self-organization.