Sommaire:

Active matter is a broad class of materials within which individual entities, the active particles, consume energy in order to perform movement. These materials are at the intersection of many distinct fields of research, such as biology, engineering, and physics, and have thus attracted considerable attention. Because of their perpetual consumption of energy, these systems are out of thermodynamic equilibrium. As a consequence they display a wealth of surprising phenomena which challenge our conception of equilibrium phases and dynamics. Among them, collective motion is particularly intriguing and exciting on multiple grounds. First because it emerges in systems with distinct length and time scales, from collections of cells to large crowds, flocks, and swarms, yet with some common characteristics. This thus suggests some sense of universality in the mechanisms leading to different collective behaviours. Second because parts of these motions display signatures shared with other equilibrium phenomena. While the latter are very diverse, ranging from the glass transition to inertial turbulence, these connections mean that a number of concepts and tools are readily available to describe out-of-equilibrium behaviours. Third because the possible applications of the understanding and control of these phenomena are far-reaching: treatment of specific pathologies, design of intelligent materials, crowd management, etc. In this Thesis, we focus on dense active matter, where the movement of individual particles is hindered by crowding effects, and aim to characterise how this competition leads to emerging collective motion. To this effect we use a simple model of two-dimensional isotropic self-propelled particles, namely active Ornstein-Uhlenbeck particles, where the departure from the equilibrium limit is controlled via the persistence time of propulsion forces. Owing to its simplicity, the phenomena described within this model have the potential to apply to a broad range of materials. We broadly map the phase behaviour of this model, from the equilibrium-like regime at small persistence to the to far-from-equilibrium regime at large persistence. We focus our efforts on the latter regime, where velocity correlations were recently shown to emerge. We demonstrate that a disordered liquid phase exists up to very large persistence, if polydispersity frustrates the ordering of the system, and that this persistent liquid displays various manifestations of disordered collective motion. First, we show that persistent systems are dynamically arrested at large packing fraction. Close to dynamical arrest, we find that the liquid displays dynamical heterogeneity similar to equilibrium dense systems. We investigate, in the idealised limit of infinite persistence, the microscopic processes leading to these heterogeneities. Then, away from dynamical arrest, we show that our model displays chaotic advection flows, as typically shown by turbulent systems. We highlight how this specific behaviour may be universal to a broader class of active systems relying on the competition of crowding and persistent forcing. Finally, in monodisperse systems which display long-range order at large packing fraction, we describe the far-from-equilibrium mechanisms leading to structural relaxation.

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