Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming.

We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, χ_{p}. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χ_{p}∝|ϕ-ϕ_{c}^{∞}|^{-γ_{p}} where ϕ_{c}^{∞} is the jamming threshold in the absence of pins.