Mean-field dynamics of infinite-dimensional particle systems: global shear versus random local forcing

Abstract

In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in Ref. [1], which consists of randomly assigning a constant local displacement on each particle, with a finite spatial correlation length. We show that, in the infinite-dimension limit, the mean-field dynamics under such a random forcing is strictly equivalent to that under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements on interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. We discuss specifically the implications on the quasistatic driving of glasses -- initially prepared at a replica-symmetric equilibrium -- and how the corresponding 'stress-strain'-like curves and the elastic moduli can be rescaled onto their quasistatic-shear counterparts. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different driven disordered systems.

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• Jamming, relaxation, and memory in a structureless glass former
• Active Jamming at Criticality
• Tuning Steady Shear Rheology through Active Dopants
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density
• Yielding in dense active matter