  We use computer simulations to study the microscopic dynamics of an athermal
assembly of soft particles near the fluid-to-solid, jamming transition.
Borrowing tools developed to study dynamic heterogeneity near glass
transitions, we discover a number of original signatures of the jamming
transition at the particle scale. We observe superdiffusive, spatially
heterogeneous, and collective particle motion over a characteristic scale which
displays a surprising non-monotonic behavior across the transition. In the
solid phase, the dynamics is an intermittent succession of elastic deformations
and plastic relaxations, which are both characterized by scale-free spatial
correlations and system size dependent dynamic susceptibilities. Our results
show that dynamic heterogeneities in dense athermal systems and glass-formers
are very different, and shed light on recent experimental reports of
`anomalous' dynamical behavior near the jamming transition of granular and
colloidal assemblies.
