# Universal relaxation dynamics of sphere packings below jamming

## TL;DR

This paper demonstrates that sphere packings below jamming exhibit a universal slow relaxation dynamics characterized by a diverging time scale, which is consistent across different packing protocols and can be measured via vibrational density of states.

## Contribution

It reveals a universal relaxation behavior and critical exponent in sphere packings below jamming, linking structure to dynamics across various physical and computational scenarios.

## Key findings

- Diverging relaxation time scale at jamming transition.
- Universal critical exponent for different packing protocols.
- Vibrational density of states encodes the slow dynamics.

## Abstract

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.