Active particles in heterogeneous media display new physics: existence of optimal noise and absence of bands and long-range order

TL;DR

This study reveals that in heterogeneous media, self-propelled particles exhibit an optimal noise level for maximum order, lack long-range order, and do not form propagating bands, indicating new physics in collective motion.

Contribution

It demonstrates the absence of bands and long-range order in heterogeneous environments and identifies an optimal noise level for collective order, revealing two critical points in the transition.

Findings

Disappearance of propagating bands in heterogeneous media

Existence of an optimal noise level for maximum order

Disorder at both high and low noise limits

Abstract

We present a detailed study of the large-scale collective properties of self-propelled particles (SPPs) moving in two-dimensional heterogeneous space. The impact of spatial heterogeneities on the ordered, collectively moving phase is investigated. We show that for strong enough spatial heterogeneity, the well-documented high-density, high-ordered propagating bands that emerge in homogeneous space disappear. Moreover, the ordered phase does not exhibit long-range order, as occurs in homogeneous systems, but rather quasi-long range order: i.e. the SPP system becomes disordered in the thermodynamical limit. For finite size systems, we find that there is an optimal noise value that maximizes order. Interestingly, the system becomes disordered in two limits, for high noise values as well as for vanishing noise. This remarkable finding strongly suggests the existence of two critical points, instead of only one, associated to the collective motion transition. Density fluctuations are consistent with these observations, being higher and anomalously strong at the optimal noise, and decreasing and crossing over to normal for high and low noise values. Collective properties are investigated in static as well as dynamic heterogeneous environments, and by changing the symmetry of the velocity alignment mechanism of the SPPs.