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

Abstract

We study an interacting high-density one-dimensional system of self-propelled particles described by the active Ornstein-Uhlenbeck particle 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 this work, we focus on a lesser-known aspect of the model, namely, its dynamical behavior. To this purpose, we investigate theoretically and numerically the time-dependent velocity autocorrelation and spatiotemporal velocity correlation functions. The study of these correlations provides a measure of the average lifetime and, thus, the stability in time of the velocity domains.

Long range correlations and slow time scales in a boundary driven granular model

“…( 1 ) cannot be mapped into an Ising or Heisenberg-like Hamiltonian system maintaining the same properties. We also note that the same scaling relation between correlation length and characteristic time of the bath has also been found in dilute granular systems with an hydrodynamic approach 44 and in dense active systems 26 . Nevertheless in these two translational invariant systems the equivalent limit for is meaningless because in the first case it removes the driving while in the second one it implies a deterministic constant self propulsion.…”

“…Lattices (particularly in 1d) bring two main advantages: (1) analytical calculations are often possible, (2) they help to isolate minimal ingredients for the occurrence of the phenomenon under study. Considering just the non-equilibrium context, 1D models have been used to study thermal conduction 20 – 22 , non-equilibrium fluctuations 23 , 24 , correlations and response with non-symmetric couplings 25 , velocity alignment in active matter 26 , systems with Vicsek-like interactions 27 , 28 , velocity fields in granular materials 29 – 31 . In the following we will just consider linear interactions between variables and this allows to work in the framework of multivariate linear stochastic processes.…”

Non-homogeneous Heating induces Scale-free Correlations and Slow time Scales in a Granular-like Velocity Field

“…1 can't be mapped into an Ising or Heisenberg-like Hamiltonian system maintaining the same properties. We also note that the same scaling relation between correlation length and characteristic time of noise has also been found in dilute granular systems with an hydrodynamic approach 42 and in dense active systems 25 . Nevertheless in these two cases the equivalent limit for α = 0 is meaningless because in the first case it removes the driving while in the second one it implies a deterministic constant self propulsion.…”

“…Lattices (particularly in 1d) bring two main advantages: (i) analytical calculations are often possible, (ii) they help to isolate minimal ingredients for the occurrence of the phenomenon under study. Considering just the non-equilibrium context, 1D models have been used to study thermal conduction [19][20][21] , non-equilibrium fluctuations 22,23 , correlations and response with arXiv:2101.09516v1 [cond-mat.stat-mech] 23 Jan 2021 non-symmetric couplings 24 , velocity alignment in active matter 25 , systems with Vicsek-like interactions 26,27 , velocity fields in granular materials [28][29][30] . In the following we'll just consider linear interactions between variables and this allows to work in the framework of multivariate linear stochastic processes.…”

Fluctuation–Dissipation Relations in Active Matter Systems

“…Its connection with other popular models for self-propelled particles has been addressed by some authors [51,52]. For instance, the AOUP model can reproduce the accumulation near the boundaries of channels and obstacles [41,53], the non-equilibrium clustering or phase-separation [25,54,55] typical of active matter and the spatial velocity correlation spontaneously observed in dense active systems [56,57]. According to the AOUP scheme, the position in d dimensions x of the self-propelled particle evolves with the following stochastic equation,…”