A microscopic mean-field theory of the jamming transition

TL;DR

This paper develops a microscopic mean-field theory for the jamming transition in dense particle packings, providing analytical scaling laws, correlation function predictions, and validation through simulations.

Contribution

It introduces a novel equilibrium statistical mechanics approach to describe athermal jamming transitions in soft particles, deriving analytical laws and testable predictions.

Findings

Derived analytical scaling laws and exponents for the jamming transition.

Predicted microscopic correlation functions for jammed states.

Confirmed predictions with computer simulations.

Abstract

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions using fully equilibrium statistical mechanics and develop a microscopic many-body mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications, and whose accuracy we confirm using computer simulations.