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

We study an interacting high-density one-dimensional system of self-propelled particles described by the Active Ornstein-Uhlenbeck particle (AOUP) model where, even in the absence of alignment interactions, velocity and energy domains spontaneously form in analogy with those already observed in two dimensions. Such domains are regions where the individual velocities are spatially correlated as a result of the interplay between self-propulsion and interactions. Their typical size is controlled by a characteristic correlation length. In the present work, we focus on a novel and lesser-known aspect of the model, namely its dynamical behavior. To this purpose, we investigate theoretically and numerically the time-dependent velocity autocorrelation and spatio-temporal velocity correlation functions. The study of these correlations provides a measure of the average life-time and, thus, the stability in time of the velocity domains.