Bridging the gap between standard jamming and the mean field theory of glasses

Jamming is both a global and local constraint satisfaction problem. Globally, the Maxwell criterion forces the average number of particles to be twice the dimension, while locally the distance metric fundamentally limits the local environment of each particle, thus producing a complex spatial embedding. Here, the Mari-Kurchan model offers a way to continuously perturb the distance metric itself by adding a unique vector shift between every pair of particles with variance Λ. In the limit Λ →0, one recovers the standard hard sphere problem where critical scaling of several quantities is highly non-trivial. Meanwhile, in the limit Λ→∞, the model becomes mean-field in nature and the critical scalings of those same quantities becomes trivial. In this talk we will investigate the effects of varying Λ on the jamming transition density in hopes of explaining the emergence of non-trivial finite size scaling in the standard hard sphere problem (Λ=0). More broadly, we will show that by allowing variations in Λ one can explore a wide class of perturbations and their unification under the recently developed dynamical mean field theory of glasses.