Constrained Fluctuations in Jammed Soft Disk Packings

Jamming, the point at which a collection of particles begins to exhibit global rigidity with increasing density has been the focus of intense research over the last decade. Jamming is ubiquitous in nature and occurs in systems ranging from mesoscopic lengthscales to macroscopic particulate matter. Although jamming transitions seem to be accompanied by 'divergences' in time-scales and length-scales, they cannot be explained using existing frameworks for phase transitions. Fluctuations in such systems are governed by microscopic constraints of force and torque balance on every particle, and are thus greatly restricted. Developing a predictive statistical mechanics framework to describe jammed systems therefore represents a new theoretical challenge. In this talk I will describe some of my research on an idealized model of soft disks in two dimensions where theoretical progress can be made.