Two diverging length scales in the structure of jammed packings

Abstract: At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $\xi_{Z}$, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, $\xi_{f}$, is associated with contact-number fluctuations in subsystems of different sizes. On scales below $\xi_{f}$ the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of $\xi_{Z}$ and $\xi_{f}$ are different and appear to be different in two and three dimensions.