Phase Transitions and superuniversality in the dynamics of a self-driven particle
arXiv:cond-mat/0607521 · doi:10.1103/PhysRevE.74.011125
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.
14 pages, 4 figures