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).