Vibrations and diverging length scales near the unjamming transition

Abstract

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction $\varphi$ is lowered towards the onset of unjamming at ${\varphi }_c$, the density of vibrational states approaches a non-zero value in the limit of zero frequency. For $\varphi >{\varphi }_c$, there is a crossover frequency, ${\omega }^{\ast }$ below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with $\varphi -{\varphi }_c$. Characteristic length scales, determined from the dominant wavevector contributing to the eigenmode at ${\omega }^{\ast }$, diverge as power-laws at the unjamming transition.

Submitted to PRL, 4 pages + 7 .eps figures