Welcome to the PCSL Research Group
Complex systems present an abundance of long-lived metastable states. They do not equilibrate easily, and therefore remember their past. Examples include glassy materials (such the glass that makes our windows, sand, spin and electron glasses) as well as dynamical systems that appear in biology (neuronal or proteins regulation networks, or ecologies). The Physics of Complex Systems Laboratory develops tools in statistical mechanics and dynamical systems to address both associated conceptual questions (such as the principles governing sampling in these non-equilibrium situations) and practical ones (e.g. how particles manage to move while avoiding each other in a crowded environment, such as a dense granular flow).
Amorphous materials: Many materials around us are amorphous, including structural glasses, granular materials, foams, colloidal suspensions, pastes and plastics. Describing them remains a central challenge of condensed matter: in their solid phase, they form glassy, out-of-equilibrium structures. In their fluid phase, they are strongly driven and thus cannot be described perturbatively around some equilibrium liquid phase. We have proposed that key aspects of both the solid and the dense liquid phase are controlled by the proximity of the jamming transition that separates these two phases. This leads to a description of the solid based on the elementary excitations governing their linear response (the “anomalous” or “soft” modes) and their plasticity (localized shear transformations if particles are soft, or rewiring of contact network if particles are hard). The dense liquid phase is then described as a dilute gas of excitations, whose concentration goes to zero as jamming is approached. We are exploring the consequences of this framework in practical situations (such as granular flows where friction raises new fundamental questions, or erosion where only a tiny layer of the material is fluidized) as well as biological settings. In particular we are investigating how proteins evolve to become machines with specific responses at a distance (allostery), building on the recent understanding of force chains and mechanical energy propagation in disordered environments.
Marginal stability: In out-of-equilibrium complex systems, states are not sampled according to the Boltzmann weight. Is there a principle to describe how sampling takes place then? Focusing on the extreme case of zero temperature dynamics, we have shown that glassy systems with sufficiently long-range interactions are marginally stable: their density of excitations at low-energy is just suppressed enough to avoid giant rearrangements every time they are perturbed. These results indicate the need to replace the old concept of “self-organized criticality” by a classification emphasizing the presence of a pseudo-gap (i.e. a vanishing density of excitations) that does imply crackling (avalanche-type response) for a range of fields. We are investigating how this classification can be extended to non-gradient dynamics (generic for example of biological settings) and applied to the failure of materials (such as the thin granular layer that controls earthquake inside the fault gouge).