  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.
