Vibrations and diverging length scales near the unjamming transition
L. E. Silbert, A. J. Liu, S. R. Nagel
Abstract
We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction ϕ is lowered towards the onset of unjamming at ϕc, the density of vibrational states approaches a non-zero value in the limit of zero frequency. For ϕ>ϕc, there is a crossover frequency, ω* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with ϕ-ϕc. Characteristic length scales, determined from the dominant wavevector contributing to the eigenmode at ω*, diverge as power-laws at the unjamming transition.
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