Out-of-equilibrium dynamics of particle systems in infinite dimension*

Dense assemblies of particles are prototypes of structurally disordered systems, such as amorphous solids or yield stress fluids. In infinite dimension their mean-field description becomes exact, and solving their equilibrium dynamics in this limit has been remarkably fruitful in capturing static properties of finite-dimensional systems as well. Here we address their out-of-equilibrium dynamics, paving the way to obtaining a similar infinite-dimensional benchmark for the mechanical or rheological properties of structurally disordered systems.
More specifically, we derive the mean-field dynamical equations that describe a system of pairwise interacting particles, in infinite dimension and in the thermodynamic limit, in a generic setting with arbitrary noise and friction kernels, and possibly under a global shear. We show that the complex many-body dynamics can then be exactly reduced to a single one-dimensional stochastic process, with three effective kernels that have to be determined self- consistently.
In this talk, I will sketch the derivation of this effective dynamics, highlighting in particular the few key ingredients of the high-dimensional physics and their possible relevance for finite-dimensional systems. Since we consider a very general setting, we can model a broad range of situations — equilibrium, quasi-statics, transients or steady-states — such as liquid and glass rheology or active self-propelled particles.

References: E. Agoritsas, T. Maimbourg & F. Zamponi, J. Phys. A 52 144002 & 334001 (2019).