  The sluggish and heterogeneous dynamics of glass forming liquids is
frequently associated to the transient coexistence of two phases of particles,
respectively with an high and low mobility. In the absence of a dynamical order
parameter that acquires a transient bimodal shape, these phases are commonly
identified empirically, which makes difficult investigating their relation with
the structural properties of the system. Here we show that the distribution of
single particle diffusivities can be accessed within a Continuous Time Random
Walk description of the intermittent motion, and that this distribution
acquires a transient bimodal shape in the deeply supercooled regime, thus
allowing for a clear identification of the two coexisting phase. In a simple
two-dimensional glass forming model, the dynamic phase coexistence is
accompanied by a striking structural counterpart: the distribution of the
crystalline-like order parameter becomes also bimodal on cooling, with
increasing overlap between ordered and immobile particles. This simple
structural signature is absent in other models, such as the three-dimesional
Kob-Andersen Lennard-Jones mixture, where more sophisticated order parameters
might be relevant. In this perspective, the identification of the two dynamical
coexisting phases opens the way to deeper investigations of structure-dynamics
correlations.
