Boundary and bulk perturbations in vectorial active matter

Abstract

Active matter, i.e., nonequilibrium systems that transform non-thermal energy from the environment into self-propulsion or other functional mechanisms, has attracted the attention of the statistical physics community in recent decades. Flocking, as shown by the aerial displays of starling flocks, is perhaps one of the most intriguing collective behaviors exhibited by active matter. While the bulk behavior of free collective motion is now fairly well understood, at least when the surrounding fluid can be neglected (the so-called dry approximation), much less is known when collective motion explicitly breaks a continuous rotational symmetry, either globally or locally. This thesis explores the effects of such explicit symmetry breaking on the dynamics of collective motion. Global symmetry breaking may arise from an anisotropic environment, where a favored direction sets the mean flocking direction. A key question addressed here is how to detect small anisotropies without prior knowledge of the underlying environmental asymmetry. The thesis then examines boundary-induced symmetry breaking. In confined flocking systems, local anisotropies arise at the boundaries and significantly affect both bulk and boundary behavior, especially in finite-sized setups. We focus in particular on a polar active fluid confined between two parallel repelling walls, showing that the influence of the boundaries extends far into the bulk. Finally, we consider a more subtle confinement inspired by the phototactic behavior of certain cyanobacteria, showing that key features of active matter, such as accumulation at boundaries, can arise even without mechanical confinement. The results shed light on how symmetry-breaking perturbations, whether imposed globally or locally, alter the dynamics of active matter systems and offer new insights into the control of collective motion.