Boundary symmetry breaking of flocking systems

TL;DR

This paper studies how confinement between parallel walls affects flocking systems, revealing boundary-induced symmetry breaking, an effective mass suppression of correlations, and enhanced order, with implications for experimental flocking setups.

Contribution

It introduces a boundary symmetry breaking mechanism in flocking systems and analyzes its effects on correlations and order parameters through scaling and simulations.

Findings

Confinement induces an effective mass term suppressing correlations.

Boundary effects align flocking direction parallel to walls.

Finite size effects influence the detectability of boundary-induced phenomena.

Abstract

We consider a flocking system confined transversally between two infinite reflecting parallel walls separated by a distance $L_\perp$. Infinite or periodic boundary conditions are assumed longitudinally to the direction of collective motion, defining a ring geometry typical of experimental realizations with flocking active colloids. Such a confinement selects a flocking state with its mean direction aligned parallel to the wall, thus breaking explicitly the rotational symmetry locally by a boundary effect. Finite size scaling analysis and numerical simulations show that confinement induces an effective mass term ${M_c} \sim L_\perp^{-\zeta}$ (with positive $\zeta$ being the dynamical scaling exponent of the free theory) suppressing scale free correlations at small wave-numbers. However, due to the finite system size in the transversal direction, this effect can only be detected for large enough longitudinal system sizes (i.e. narrow ring geometries). Furthermore, in the longitudinal direction, density correlations are characterized by an anomalous effective mass term. The effective mass term also enhances the global scalar order parameter and suppresses fluctuations of the mean flocking direction. These results suggest an equivalence between transversal confinement and driving by an homogeneous external field, which breaks the rotational symmetry at the global level.