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We demonstrate that a system of self-propelled particles (SPP) exhibitsspontaneous symmetry breaking and self-organization in one dimension, incontrast with previous analytical predictions. To explain this surprisingresult we derive a new continuum theory that can account for the development ofthe symmetry broken state and belongs to the same universality class as thediscrete SPP model.

Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension