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

TL;DR

This paper investigates the dynamical properties of one-dimensional active matter systems, focusing on velocity correlations and domain stability, revealing insights into the temporal behavior of self-propelled particles.

Contribution

It introduces a detailed analysis of the time-dependent velocity correlations in a one-dimensional AOUP model, highlighting the dynamical stability of velocity domains.

Findings

Velocity and energy domains spontaneously form in 1D active matter.

Correlation functions reveal the lifetime and stability of velocity domains.

The study combines theoretical and numerical approaches to analyze dynamics.

Abstract

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.