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We study an interacting high-density one-dimensional system of self-propelledparticles described by the Active Ornstein-Uhlenbeck particle (AOUP) modelwhere, even in the absence of alignment interactions, velocity and energydomains spontaneously form in analogy with those already observed in twodimensions. Such domains are regions where the individual velocities arespatially correlated as a result of the interplay between self-propulsion andinteractions. Their typical size is controlled by a characteristic correlationlength. In the present work, we focus on a novel and lesser-known aspect of themodel, namely its dynamical behavior. To this purpose, we investigatetheoretically and numerically the time-dependent velocity autocorrelation andspatio-temporal velocity correlation functions. The study of these correlationsprovides a measure of the average life-time and, thus, the stability in time ofthe velocity domains.

Time-dependent properties of interacting active matter: dynamical behavior of one-dimensional systems of self-propelled particles