Noise-induced breakdown in linear self-driven particle systems

Self-driven particle systems can describe many self-organized phenomena. Prominentexamples are oscillation, wave, lane, or band formations, among other swarming andcoordinated movements. Collective dynamics are classically understood in the literature of active matter as motility-induced phase separation using meta-stable non-linear in-teraction models. Critical settings of the parameters separate the disorder states from non-uniform dynamics describing macroscopic patterns and structures. We show in this contribution that noise effects can initiate the spontaneous formation of waves insingle-file motions of self-driven particles. In contrast to usual modeling approaches, no non-linear interaction mechanisms or phase transitions are necessary to coordinate the dynamics. The stochastic effects initiate the self-organization in the second order in a purely linear and ergodic framework. The coupling of the noise to a discrete gradient in space yields the emergence of stop-and-go waves, which we characterize using speed and spacing auto-correlation functions. Varying the characteristics of the noise allows for obtaining rich dynamics ranging from coupled dynamics and stable homogeneous dynamics to stop-and-go patterns with deterministic oscillating features