Criticality and Scaling around the Jamming Transition

The jamming transition of athermal soft spheres provides a starting point for understanding the mechanical and thermal properties of disordered solids. Despite being a highly idealized model, this non-equilibrium critical point exhibits very rich physics, including power-law scaling, multiple diverging length scales, and finite size effects. I will show how our understanding of these behaviors can be unified through a Widow-like scaling ansatz. In addition to predicting novel scaling behaviors, this ansatz provides a framework for connecting the physics of the jamming transition to more realistic systems by, for example, including temperature, friction, or long-ranged attractions. I will also outline some new techniques for probing both the critical and non-critical behavior in these more generalized frameworks.