Disordered surface vibrations in jammed sphere packings

TL;DR

This study investigates how free surfaces in disordered jammed sphere packings influence vibrational modes, revealing surface-specific low-frequency modes with decay lengths diverging near the jamming transition.

Contribution

It uncovers the existence and properties of surface vibrational modes in jammed packings, extending understanding of vibrational behavior near free surfaces in disordered systems.

Findings

Surface vibrational modes extend below bulk frequency scale $\omega^*$.

Number of surface modes scales with $\Delta Z$.

Decay lengths diverge as $\Delta Z^{-1/2}$ and $\Delta Z^{-1}$ approaching jamming.

Abstract

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale $\omega^*$. This frequency is controlled by $\Delta Z = \langle Z \rangle - 2d$, the difference between the average coordination of the spheres and twice the spatial dimension, $d$, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below $\omega^*$. The total number of these low-frequency surface modes is controlled by $\Delta Z$, and the profile of their decay into the bulk has two characteristic length scales, which diverge as $\Delta Z^{-1/2}$ and $\Delta Z^{-1}$ as the jamming transition is approached.