Phase Transitions and superuniversality in the dynamics of a self-driven particle

TL;DR

This paper investigates a self-driven particle model where a particle's movement, influenced by a self-generated field, exhibits phase transitions and superuniversality, revealing dimension-independent behavior and a shift from diffusion to diverging diffusion at critical coupling.

Contribution

It introduces a novel active random walker model with a self-generated field, demonstrating phase transitions and superuniversality in its dynamics.

Findings

Identifies a phase transition from diffusion to diverging diffusion at critical coupling.

Shows dynamics are independent of dimension and noise amplitude.

Reveals superuniversality in the particle's behavior across different conditions.

Abstract

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.